International Conference on Computational Science (ICCS 2017) Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations G. Bernabé † , J. C. Cano ‡ , J. Cuenca † , A. Flores † , D. Giménez ‡ , M. Saura-Sánchez Ω and P. Segado-Cabezos Ω † Computer Engineering Department, University of Murcia ‡ Computer Science and Systems Department, University of Murcia Ω Mechanical Engineering, Technical University of Cartagena 12-14 June, 2017 Conference title 1
Outline Introduction and Motivation Parallelism in the Structural Groups method Results Conclusions and Future work ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 2
Outline Introduction and Motivation Parallelism in the Structural Groups method Results Conclusions and Future work ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 3
Introduction • Multibody systems (MBS): mechanical systems formed by rigid and flexible bodies which are connected by means of mechanical joins in such a way that there is relative movement between their bodies terminal handles platform The Stewart Platform ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 4
Introduction • The study of the relationships between the bodies is known as kinematic modeling • Selects a vector q of coordinates to define the position and orientation of each body of the MBS in the space • Coordinates are related by means a nonlinear systems of constrainst equations Φ (q) = 0 ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 5
Introduction • The study of the relationships between the bodies is known as kinematic modeling • Selects a vector q of coordinates to define the position and orientation of each body of the MBS in the space • Coordinates are related by means a nonlinear systems of constrainst equations Φ (q) = 0 Global Topogical formulations formulations ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 6
Introduction • The study of the relationships between the bodies is known as kinematic modeling • Selects a vector q of coordinates to define the position and orientation of each body of the MBS in the space • Coordinates are related by means a nonlinear systems of constrainst equations Φ (q) = 0 exploits the topology of the MBS to reduce the dimension of the problem Global Topogical by relating the position of formulations formulations each body with respect to its preceding one ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 7
Introduction • Structural Analysis: splits the MBS into Structural Groups (SGs) • Kinematic Structure: How many SG, kind & order terminal (SG-T0) (8) 12 dependent coordinates handle-stick (SG-H) (2-7) 15 dependent coordinates The Stewart Platform ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 9
Introduction • Structural Analysis: splits the MBS into Structural Groups (SGs) • Kinematic Structure: How many SG, kind & order terminal (SG-T) (8) handle-stick (SG-H) (2-7) ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 10
Motivation 1. A simulator for the computational kinematic analysis of MBS to allow us to analyze the efficiency of the group equations 2. A better exploitation of the computer resources by applying parallelism to reduce the executions in real-time applications terminal (SG-T) (8) handle-stick (SG-H) (2-7) ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 11
Outline Introduction and Motivation Parallelism in the Structural Groups method Results Conclusions and Future work ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 12
Outline Introduction and Motivation Parallelism in the Structural Groups method Results Conclusions and Future work ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 13
Parallelism in the Structural Groups method • The Stewart Platform (MBS) is a case study to analyze the application of parallelism for speeding up the kinematic analysis based on Group equations terminal (SG-T) (8) handle-stick (SG-H) (2-7) ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 14
Parallelism in the Structural Groups method • A scheme of the Group Equations method 1 for number of external iterations (tEnd*dt) do 2 Solve kinematic of terminal (size nSG-T) //MKL p. 3 for all structural components (nSG) do //OpenMP p. 4 for number of internal iterations (tEnd2) do 5 Solve kinematic of SC (size nSG-HS) //MKL p. 6 end for 7 end for 8 end for ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 15
Parallelism in the Structural Groups method • A scheme of the Group Equations method 1 for number of external iterations (tEnd*dt) do 2 Solve kinematic of terminal (size nSG-T) //MKL p. 3 for all structural components (nSG) do //OpenMP p. 4 for number of internal iterations (tEnd2) do 5 Solve kinematic of SC (size nSG-HS) //MKL p. 6 end for tEnd: a maximum execution time is established dt: time step 7 end for tEnd2: number of iterations for the position problem nSG: number of structural groups 8 end for nSG-T: dimension of the SG-T matrix nSG-HS: dimension of the SG-HS matrix ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 16
Parallelism in the Structural Groups method Parallelism can be exploited by simultaneously solving • A scheme of the Group Equations method the problems for the SGs in the system, inside a multicore system (MKL) or 1 for number of external iterations (tEnd*dt) do with calls to GPU (MAGMA) 2 Solve kinematic of terminal (size nSG-T) //MKL p. 3 for all structural components (nSG) do //OpenMP p. 4 for number of internal iterations (tEnd2) do 5 Solve kinematic of SC (size nSG-HS) //MKL p. 6 end for tEnd: a maximum execution time is established dt: time step 7 end for tEnd2: number of iterations for the position problem nSG: number of structural groups 8 end for nSG-T: dimension of the SG-T matrix nSG-HS: dimension of the SG-HS matrix ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 17
Parallelism in the Structural Groups method • A scheme of the Group Equations method 1 for number of external iterations (tEnd*dt) do 2 Solve kinematic of terminal (size nSG-T) //MKL p. 3 for all structural components (nSG) do //OpenMP p. 4 for number of internal iterations (tEnd2) do 5 Solve kinematic of SC (size nSG-HS) //MKL p. 6 end for 7 end for 8 end for • We have exploited the parallelism in different ways: 1. GEMKL: The multithreading version of MKL. 2. GEOMP+MKL: OpenMP is used to start the threads which works simultaneously in the solution of different SGs. The matrix problems for each group are solved by calling MKL, which can be sequential or multithreading 3. GEOMP+MA27: OpenMP parallelism is exploited, with calls to the routine MA27 for solution of the matrix problem 4. GEMAGMA: GPU parallelism is exploited by solving the matrix problems with MAGMA. ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 18
Outline Introduction Parallelism in the Structural Groups method Results Conclusions and Future work ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 19
Outline Introduction Parallelism in the Structural Groups method Results Conclusions and Future work ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 20
Results • CPU Intel Core i5-2400 3.10 GHz – 4 cores – No Hyper-Threading – 16 GB RAM • MKL GMKL and MA27 GMA27 (dense and sparse solvers) is used for the Global formulation • GEOMP+MKL and GEOMP+MA27 is used for the Group equations (Topological formulation) ICCS’17 – Exploiting Hybrid Parallelism in the Kinematic Analysis of Multibody Systems Based on Group Equations 21
Recommend
More recommend
