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A presentation of the library OFELI Rachid Touzani Laboratoire de Math ematiques Universit e Blaise Pascal Clermont-Ferrand, France OFELI Presentation R. Touzani 1/20 Introduction An example of a finite element code Structure of the

  1. Introduction An example of a finite element code Structure of the library The OFELI package Levels of use of the library • Level 0: No knowledge of C++ is required. Use of prototype programs (Demos) • Level 1: Programming of finite element codes using OFELI classes. Possible contribution with classes and functions = ⇒ Contribution to Demo programs • Level 2: Contribution to the library’s kernel by Implementing equations classes and solvers, . . . What are objects in a finite element code ? Mathematical entities that one manipulates when solving a problem: Mesh, matrices, vectors, equations, solvers (nonlinear problems, optimization, . . . ), . . . OFELI Presentation R. Touzani 4/20

  2. Introduction An example of a finite element code Structure of the library The OFELI package Levels of use of the library • Level 0: No knowledge of C++ is required. Use of prototype programs (Demos) • Level 1: Programming of finite element codes using OFELI classes. Possible contribution with classes and functions = ⇒ Contribution to Demo programs • Level 2: Contribution to the library’s kernel by Implementing equations classes and solvers, . . . What are objects in a finite element code ? Mathematical entities that one manipulates when solving a problem: Mesh, matrices, vectors, equations, solvers (nonlinear problems, optimization, . . . ), . . . OFELI Presentation R. Touzani 4/20

  3. Introduction An example of a finite element code Structure of the library The OFELI package Levels of use of the library • Level 0: No knowledge of C++ is required. Use of prototype programs (Demos) • Level 1: Programming of finite element codes using OFELI classes. Possible contribution with classes and functions = ⇒ Contribution to Demo programs • Level 2: Contribution to the library’s kernel by Implementing equations classes and solvers, . . . What are objects in a finite element code ? Mathematical entities that one manipulates when solving a problem: Mesh, matrices, vectors, equations, solvers (nonlinear problems, optimization, . . . ), . . . OFELI Presentation R. Touzani 4/20

  4. Introduction An example of a finite element code Structure of the library The OFELI package Levels of use of the library • Level 0: No knowledge of C++ is required. Use of prototype programs (Demos) • Level 1: Programming of finite element codes using OFELI classes. Possible contribution with classes and functions = ⇒ Contribution to Demo programs • Level 2: Contribution to the library’s kernel by Implementing equations classes and solvers, . . . What are objects in a finite element code ? Mathematical entities that one manipulates when solving a problem: Mesh, matrices, vectors, equations, solvers (nonlinear problems, optimization, . . . ), . . . OFELI Presentation R. Touzani 4/20

  5. Introduction An example of a finite element code Structure of the library The OFELI package An example of program Consider the following boundary value problem: in Ω ⊂ R 2 (or R 3 ) ∆ u = 0 u = g on ∂ Ω Matrix Formulation Au = b where � a ij = ∇ φ j · ∇ φ i d x Ω Boundary Conditions: We enforce u = g by a penalty technique: i − 1 N � � a ij u j + a ij u j + λ a ii u i = λ a ii g ( x i ) λ ≫ 1 j =1 j = i +1 for each node i on the boundary. OFELI Presentation R. Touzani 5/20

  6. Introduction An example of a finite element code Structure of the library The OFELI package An example of program Consider the following boundary value problem: in Ω ⊂ R 2 (or R 3 ) ∆ u = 0 u = g on ∂ Ω Matrix Formulation Au = b where � a ij = ∇ φ j · ∇ φ i d x Ω Boundary Conditions: We enforce u = g by a penalty technique: i − 1 N � � a ij u j + a ij u j + λ a ii u i = λ a ii g ( x i ) λ ≫ 1 j =1 j = i +1 for each node i on the boundary. OFELI Presentation R. Touzani 5/20

  7. Introduction An example of a finite element code Structure of the library The OFELI package An example of program Consider the following boundary value problem: in Ω ⊂ R 2 (or R 3 ) ∆ u = 0 u = g on ∂ Ω Matrix Formulation Au = b where � a ij = ∇ φ j · ∇ φ i d x Ω Boundary Conditions: We enforce u = g by a penalty technique: i − 1 N � � a ij u j + a ij u j + λ a ii u i = λ a ii g ( x i ) λ ≫ 1 j =1 j = i +1 for each node i on the boundary. OFELI Presentation R. Touzani 5/20

  8. Introduction An example of a finite element code Structure of the library The OFELI package An example of program Consider the following boundary value problem: in Ω ⊂ R 2 (or R 3 ) ∆ u = 0 u = g on ∂ Ω Matrix Formulation Au = b where � a ij = ∇ φ j · ∇ φ i d x Ω Boundary Conditions: We enforce u = g by a penalty technique: i − 1 N � � a ij u j + a ij u j + λ a ii u i = λ a ii g ( x i ) λ ≫ 1 j =1 j = i +1 for each node i on the boundary. OFELI Presentation R. Touzani 5/20

  9. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  10. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  11. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  12. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  13. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  14. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  15. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  16. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  17. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  18. Introduction An example of a finite element code Structure of the library The OFELI package #include "OFELI.h" #include "Therm.h" using namespace OFELI; int main() { Mesh ms("test.m"); SkSMatrix<double> A(ms); Vect<double> b(ms.getNbDOF()), bc(ms.getNbDOF()); // Initialize bc MeshElements(ms) { DC2DT3 eq(theElement); eq.Diffusion(); eq.ElementAssembly(A); } A.Prescribe(ms,b,bc); A.Factor(); A.Solve(b); cout << b; return 0; } OFELI Presentation R. Touzani 6/20

  19. Introduction An example of a finite element code Structure of the library The OFELI package Classes in OFELI Some conventions • Class names always begin with a capital letter. • Member function names begin with capital letters except if the name starts with a verb. et les get... . • Class members that modify a class have generally names that start with the verb set ( e.g., setSize() ) • Class members that return an information have generally names that start with the verb get . ( e.g., getNbNodes() ) • Most of classes have an overload of the operator << OFELI Presentation R. Touzani 7/20

  20. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  21. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  22. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  23. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  24. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  25. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  26. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  27. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  28. Introduction An example of a finite element code Structure of the library The OFELI package To each phase in the procedure corresponds a family of classes : 1. Mesh classes Construction of a mesh: Mesh ms("test.m"); Output of a mesh : cout << ms; Loop over elements: for (ms.topElement(); (theElement=ms.getElement());) cout << *theElement; or equivalently: MeshElements(ms) Get pointer to a node: Node *nd = el->getPtrNode(2); Creation of boundary sides: ms.getBoundarySides(); Creation of all sides: ms.getAllSides(); Change of unknown support: ms.setDOFSupport(SIDE DOF); OFELI Presentation R. Touzani 8/20

  29. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  30. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  31. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  32. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  33. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  34. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  35. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  36. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  37. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  38. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  39. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes A wide variety of Template classes for vectors The template parameter is the data type for vector entries A vector class called Vect<T > . Class Vect<T > : Construction of a vector: Vect<double> v(ms.getNbNodes()); Assignment: v(1) = 5; v[0] = 5; v = -10; Other operations: v += w; v *= 5; Assembly: v.Assembly(el,ve); Euclidean norm: double x = v.getNorm2(); Vector size: int n = v.getSize(); OFELI Presentation R. Touzani 9/20

  40. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes: Class NodeVect<T > : “Node” oriented vector Construction of a vector: NodeVect<double> v(ms); NodeVect(Mesh &mesh, const Vect<T > &v, int nb dof, int first dof, char *name, double time); Assignment: v(n,i) = 5; Class ElementVect<T > : “Element” oriented vector Class SideVect<T > : “Side” oriented vector Class LocalVect<T ,N > : Small size vector LocalVect<double,4> v; OFELI Presentation R. Touzani 10/20

  41. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes: Class NodeVect<T > : “Node” oriented vector Construction of a vector: NodeVect<double> v(ms); NodeVect(Mesh &mesh, const Vect<T > &v, int nb dof, int first dof, char *name, double time); Assignment: v(n,i) = 5; Class ElementVect<T > : “Element” oriented vector Class SideVect<T > : “Side” oriented vector Class LocalVect<T ,N > : Small size vector LocalVect<double,4> v; OFELI Presentation R. Touzani 10/20

  42. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes: Class NodeVect<T > : “Node” oriented vector Construction of a vector: NodeVect<double> v(ms); NodeVect(Mesh &mesh, const Vect<T > &v, int nb dof, int first dof, char *name, double time); Assignment: v(n,i) = 5; Class ElementVect<T > : “Element” oriented vector Class SideVect<T > : “Side” oriented vector Class LocalVect<T ,N > : Small size vector LocalVect<double,4> v; OFELI Presentation R. Touzani 10/20

  43. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes: Class NodeVect<T > : “Node” oriented vector Construction of a vector: NodeVect<double> v(ms); NodeVect(Mesh &mesh, const Vect<T > &v, int nb dof, int first dof, char *name, double time); Assignment: v(n,i) = 5; Class ElementVect<T > : “Element” oriented vector Class SideVect<T > : “Side” oriented vector Class LocalVect<T ,N > : Small size vector LocalVect<double,4> v; OFELI Presentation R. Touzani 10/20

  44. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes: Class NodeVect<T > : “Node” oriented vector Construction of a vector: NodeVect<double> v(ms); NodeVect(Mesh &mesh, const Vect<T > &v, int nb dof, int first dof, char *name, double time); Assignment: v(n,i) = 5; Class ElementVect<T > : “Element” oriented vector Class SideVect<T > : “Side” oriented vector Class LocalVect<T ,N > : Small size vector LocalVect<double,4> v; OFELI Presentation R. Touzani 10/20

  45. Introduction An example of a finite element code Structure of the library The OFELI package 2. Vector classes: Class NodeVect<T > : “Node” oriented vector Construction of a vector: NodeVect<double> v(ms); NodeVect(Mesh &mesh, const Vect<T > &v, int nb dof, int first dof, char *name, double time); Assignment: v(n,i) = 5; Class ElementVect<T > : “Element” oriented vector Class SideVect<T > : “Side” oriented vector Class LocalVect<T ,N > : Small size vector LocalVect<double,4> v; OFELI Presentation R. Touzani 10/20

  46. Introduction An example of a finite element code Structure of the library The OFELI package 3. Matrix classes: Template classes for storage and manipulation of matrices using principal storage types: • Dense storage: DMatrix<T > and DSMatrix<T > • Skyline storage: SkMatrix<T > and SkSMatrix<T > • Sparse storage: SpMatrix<T > • TrMatrix<T > , LocalMatrix<T ,NR ,NC > , . . . OFELI Presentation R. Touzani 11/20

  47. Introduction An example of a finite element code Structure of the library The OFELI package 3. Matrix classes: Template classes for storage and manipulation of matrices using principal storage types: • Dense storage: DMatrix<T > and DSMatrix<T > • Skyline storage: SkMatrix<T > and SkSMatrix<T > • Sparse storage: SpMatrix<T > • TrMatrix<T > , LocalMatrix<T ,NR ,NC > , . . . OFELI Presentation R. Touzani 11/20

  48. Introduction An example of a finite element code Structure of the library The OFELI package 3. Matrix classes: Template classes for storage and manipulation of matrices using principal storage types: • Dense storage: DMatrix<T > and DSMatrix<T > • Skyline storage: SkMatrix<T > and SkSMatrix<T > • Sparse storage: SpMatrix<T > • TrMatrix<T > , LocalMatrix<T ,NR ,NC > , . . . OFELI Presentation R. Touzani 11/20

  49. Introduction An example of a finite element code Structure of the library The OFELI package 3. Matrix classes: Template classes for storage and manipulation of matrices using principal storage types: • Dense storage: DMatrix<T > and DSMatrix<T > • Skyline storage: SkMatrix<T > and SkSMatrix<T > • Sparse storage: SpMatrix<T > • TrMatrix<T > , LocalMatrix<T ,NR ,NC > , . . . OFELI Presentation R. Touzani 11/20

  50. Introduction An example of a finite element code Structure of the library The OFELI package 3. Matrix classes: Template classes for storage and manipulation of matrices using principal storage types: • Dense storage: DMatrix<T > and DSMatrix<T > • Skyline storage: SkMatrix<T > and SkSMatrix<T > • Sparse storage: SpMatrix<T > • TrMatrix<T > , LocalMatrix<T ,NR ,NC > , . . . OFELI Presentation R. Touzani 11/20

  51. Introduction An example of a finite element code Structure of the library The OFELI package 3. Matrix classes: Template classes for storage and manipulation of matrices using principal storage types: • Dense storage: DMatrix<T > and DSMatrix<T > • Skyline storage: SkMatrix<T > and SkSMatrix<T > • Sparse storage: SpMatrix<T > • TrMatrix<T > , LocalMatrix<T ,NR ,NC > , . . . OFELI Presentation R. Touzani 11/20

  52. Introduction An example of a finite element code Structure of the library The OFELI package 4. Equation classes: • An element equation is an object • Each term of the equation is a member of the class that contributes to the left and/or the right-hand side • OFELI contains a collection of classes specific to problems: • Laplace : Various numerical methods to solve the Laplace equation • Therm: Diffusion-convection problem with phase change • Solid: Elasticity problem • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Electromagnetic and Eddy Current problems • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 12/20

  53. Introduction An example of a finite element code Structure of the library The OFELI package 4. Equation classes: • An element equation is an object • Each term of the equation is a member of the class that contributes to the left and/or the right-hand side • OFELI contains a collection of classes specific to problems: • Laplace : Various numerical methods to solve the Laplace equation • Therm: Diffusion-convection problem with phase change • Solid: Elasticity problem • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Electromagnetic and Eddy Current problems • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 12/20

  54. Introduction An example of a finite element code Structure of the library The OFELI package 4. Equation classes: • An element equation is an object • Each term of the equation is a member of the class that contributes to the left and/or the right-hand side • OFELI contains a collection of classes specific to problems: • Laplace : Various numerical methods to solve the Laplace equation • Therm: Diffusion-convection problem with phase change • Solid: Elasticity problem • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Electromagnetic and Eddy Current problems • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 12/20

  55. Introduction An example of a finite element code Structure of the library The OFELI package 4. Equation classes: • An element equation is an object • Each term of the equation is a member of the class that contributes to the left and/or the right-hand side • OFELI contains a collection of classes specific to problems: • Laplace : Various numerical methods to solve the Laplace equation • Therm: Diffusion-convection problem with phase change • Solid: Elasticity problem • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Electromagnetic and Eddy Current problems • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 12/20

  56. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  57. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  58. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  59. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  60. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  61. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  62. Introduction An example of a finite element code Structure of the library The OFELI package 5. Shape function classes: To each finite element interpolation corresponds a class (e.g., 3-Node triangles ( P 1 ): Triang3 ) Available shape function classes: Line2 , Line3 , Triang3 , Triang6S , Quad4 , Tetra4 , Hexa8 . 6. Solvers: OFELI contains some template functions enabling the solution of specific problems. • Direct and iterative solvers (with preconditioners) for linear systems • Optimization problems can be solved by using a template function. The Objective function and its gradient are given through a user defined class. OFELI Presentation R. Touzani 13/20

  63. Introduction An example of a finite element code Structure of the library The OFELI package Handling of material properties: • Each material is defined in a file having its name (e.g., Copper.md). • A user can defined his own material file. • A generic material enables giving standard properties of a material. OFELI Presentation R. Touzani 14/20

  64. Introduction An example of a finite element code Structure of the library The OFELI package Handling of material properties: • Each material is defined in a file having its name (e.g., Copper.md). • A user can defined his own material file. • A generic material enables giving standard properties of a material. OFELI Presentation R. Touzani 14/20

  65. Introduction An example of a finite element code Structure of the library The OFELI package Handling of material properties: • Each material is defined in a file having its name (e.g., Copper.md). • A user can defined his own material file. • A generic material enables giving standard properties of a material. OFELI Presentation R. Touzani 14/20

  66. Introduction An example of a finite element code Structure of the library The OFELI package Handling of material properties: • Each material is defined in a file having its name (e.g., Copper.md). • A user can defined his own material file. • A generic material enables giving standard properties of a material. OFELI Presentation R. Touzani 14/20

  67. Introduction An example of a finite element code Structure of the library The OFELI package Data structures in OFELI OFELI use the XML syntax for all input and output files. All types of data are to be introduced by means of an XML tag:Various data files can be used: Project : To introduce various parameters for a main program Domain : To describe a domain via its geometric properties (for 2-D mesh generation) Mesh : To describe mesh data Material : To describe properties of a material ( i.e. a used defined material) Field : To give any input or output field (by nodes, elements or sides). A typical XML OFELI File <?xml version="1.0" encoding="ISO-8859-1" ?> <OFELI File> <info> <title></title> <date></date> <author></author> </info> ... ... </OFELI File> OFELI Presentation R. Touzani 15/20

  68. Introduction An example of a finite element code Structure of the library The OFELI package Data structures in OFELI OFELI use the XML syntax for all input and output files. All types of data are to be introduced by means of an XML tag:Various data files can be used: Project : To introduce various parameters for a main program Domain : To describe a domain via its geometric properties (for 2-D mesh generation) Mesh : To describe mesh data Material : To describe properties of a material ( i.e. a used defined material) Field : To give any input or output field (by nodes, elements or sides). A typical XML OFELI File <?xml version="1.0" encoding="ISO-8859-1" ?> <OFELI File> <info> <title></title> <date></date> <author></author> </info> ... ... </OFELI File> OFELI Presentation R. Touzani 15/20

  69. Introduction An example of a finite element code Structure of the library The OFELI package Data structures in OFELI OFELI use the XML syntax for all input and output files. All types of data are to be introduced by means of an XML tag:Various data files can be used: Project : To introduce various parameters for a main program Domain : To describe a domain via its geometric properties (for 2-D mesh generation) Mesh : To describe mesh data Material : To describe properties of a material ( i.e. a used defined material) Field : To give any input or output field (by nodes, elements or sides). A typical XML OFELI File <?xml version="1.0" encoding="ISO-8859-1" ?> <OFELI File> <info> <title></title> <date></date> <author></author> </info> ... ... </OFELI File> OFELI Presentation R. Touzani 15/20

  70. Introduction An example of a finite element code Structure of the library The OFELI package An example of mesh file: <?xml version="1.0" encoding="ISO-8859-1" ?> <OFELI File> <info> <title></title> <date></date> <author></author> </info> <Mesh dim="2"> <Nodes> 0.00 0.00 2 1.00 0.00 0 1.00 1.00 2 0.00 1.00 0 0.50 0.50 1 </Nodes> <Elements shape="triangle" nodes="3"> 1 2 5 2 3 5 3 4 5 3 4 5 4 1 5 </Elements> </Mesh> </OFELI File> OFELI Presentation R. Touzani 16/20

  71. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  72. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  73. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  74. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  75. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  76. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  77. Introduction An example of a finite element code Structure of the library The OFELI package The OFELI package The OFELI library is free and under the GPL license (GNU General Public License). It is available on the web site http://www.ofeli.net. The package contains: 1 Source files of the library (kernel + problem dependent classes: Laplace, Thermics, Solid mechanics, Fluid dynamics, Electromagnetics). 2 Documentation in HTML and PDF. The documentation is automatically generated by doxygen. 3 A tutorial with examples of finite element codes with increasing difficulty 4 Demos: Multiple finite element programs 5 A mesh generator for 2–D meshes 6 Utility programs: conversion OFELI Presentation R. Touzani 17/20

  78. Introduction An example of a finite element code Structure of the library The OFELI package The Demos These are partitioned in physical problems: • Therm: Diffusion–Convection (steady state and transient) • Solid: Linear Elasticity 2–D et 3–D • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Helmholtz and Eddy Current equations s in 2–D • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 18/20

  79. Introduction An example of a finite element code Structure of the library The OFELI package The Demos These are partitioned in physical problems: • Therm: Diffusion–Convection (steady state and transient) • Solid: Linear Elasticity 2–D et 3–D • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Helmholtz and Eddy Current equations s in 2–D • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 18/20

  80. Introduction An example of a finite element code Structure of the library The OFELI package The Demos These are partitioned in physical problems: • Therm: Diffusion–Convection (steady state and transient) • Solid: Linear Elasticity 2–D et 3–D • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Helmholtz and Eddy Current equations s in 2–D • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 18/20

  81. Introduction An example of a finite element code Structure of the library The OFELI package The Demos These are partitioned in physical problems: • Therm: Diffusion–Convection (steady state and transient) • Solid: Linear Elasticity 2–D et 3–D • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Helmholtz and Eddy Current equations s in 2–D • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 18/20

  82. Introduction An example of a finite element code Structure of the library The OFELI package The Demos These are partitioned in physical problems: • Therm: Diffusion–Convection (steady state and transient) • Solid: Linear Elasticity 2–D et 3–D • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Helmholtz and Eddy Current equations s in 2–D • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 18/20

  83. Introduction An example of a finite element code Structure of the library The OFELI package The Demos These are partitioned in physical problems: • Therm: Diffusion–Convection (steady state and transient) • Solid: Linear Elasticity 2–D et 3–D • Fluid: Incompressible Navier-Stokes equations • Electromagnetics: Helmholtz and Eddy Current equations s in 2–D • CL: Systems of Conservation Laws OFELI Presentation R. Touzani 18/20

  84. Introduction An example of a finite element code Structure of the library The OFELI package The utilities • Conversion of mesh files issued from: EasyMesh, EMC2, BAMG, Netgen, Gmsh, Gambit, Triangle and Matlab • Conversion of mesh and output files issued from: Matlab, Tecplot, Gnuplot and Paraview (VTK) • Generation of 2-D meshes by BAMG ou Triangle OFELI Presentation R. Touzani 19/20

  85. Introduction An example of a finite element code Structure of the library The OFELI package The utilities • Conversion of mesh files issued from: EasyMesh, EMC2, BAMG, Netgen, Gmsh, Gambit, Triangle and Matlab • Conversion of mesh and output files issued from: Matlab, Tecplot, Gnuplot and Paraview (VTK) • Generation of 2-D meshes by BAMG ou Triangle OFELI Presentation R. Touzani 19/20

  86. Introduction An example of a finite element code Structure of the library The OFELI package The utilities • Conversion of mesh files issued from: EasyMesh, EMC2, BAMG, Netgen, Gmsh, Gambit, Triangle and Matlab • Conversion of mesh and output files issued from: Matlab, Tecplot, Gnuplot and Paraview (VTK) • Generation of 2-D meshes by BAMG ou Triangle OFELI Presentation R. Touzani 19/20

  87. Introduction An example of a finite element code Structure of the library The OFELI package The utilities • Conversion of mesh files issued from: EasyMesh, EMC2, BAMG, Netgen, Gmsh, Gambit, Triangle and Matlab • Conversion of mesh and output files issued from: Matlab, Tecplot, Gnuplot and Paraview (VTK) • Generation of 2-D meshes by BAMG ou Triangle OFELI Presentation R. Touzani 19/20

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