Summer School CEA-EDF-INRIA Toward petaflop numerical simulation on parallel hybrid architectures BigDFT and INRIA C ENTRE DE R ECHERCHE GPU S OPHIA A NTIPOLIS , F RANCE Atomistic Simulations DFT Wavelet-Based DFT calculations on Massively Ab initio codes BigDFT Parallel Hybrid Architectures Properties BigDFT and GPUs Code details BigDFT and HPC Luigi Genovese GPU Practical cases Discussion L_Sim – CEA Grenoble Messages June 9, 2011 Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Outline Review of Atomistic Simulations 1 Density Functional Theory Ab initio codes The BigDFT project 2 BigDFT and GPU Formalism and properties Atomistic The needs for hybrid DFT codes Simulations Main operations, parallelisation DFT Ab initio codes BigDFT Performance evaluation 3 Properties Evaluating GPU gain BigDFT and GPUs Code details Practical cases BigDFT and HPC GPU Concrete examples 4 Practical cases Messages Discussion Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Review of Atomistic Simulations A interdisciplinary domain Theory – Experiment – Simulation Hardware – Computers Algorithms BigDFT and GPU Atomistic Different Atomistic Simulations Simulations DFT Force fields (interatomic potentials) Ab initio codes BigDFT Tight Binding Methods Properties BigDFT and GPUs Hartree-Fock Code details BigDFT and Density Functional Theory HPC GPU Configuration interactions Practical cases Discussion Quantum Monte-Carlo Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Quantum mechanics for many particle systems Can we do quantum mechanics on systems of many atoms? Decoupling of the nuclei and electron dynamics Born-Oppenheimer approximation: The position of the nuclei can be considered as fixed, obtaining the potential “felt” by the electrons BigDFT and GPU n Z a ∑ V ext ( r , { R 1 , ··· , R n } ) = − Atomistic | r − R a | Simulations a = 1 DFT Ab initio codes Electronic Schrödinger equation BigDFT Properties The system properties are described by the ground state BigDFT and GPUs Code details wavefunction ψ ( r 1 , ··· , r N ) , which solves Schrödinger BigDFT and HPC equation GPU H [ { R } ] ψ = E ψ Practical cases Discussion The quantum hamiltonian depends on the set of the atomic Messages positions { R } . Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Atomistic Simulations Two intrinsic difficulties for numerical atomistic simulations, related to complexity: Interactions The way that atoms interact is known: i ℏ ∂ Ψ ∂ t = H Ψ H ψ = E 0 ψ BigDFT and GPU Exploration of the configuration space Atomistic Simulations DFT Ab initio codes BigDFT Properties BigDFT and GPUs Code details BigDFT and HPC GPU Practical cases Discussion Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Atomistic Simulations Two intrinsic difficulties for numerical atomistic simulations, related to complexity: Interactions The way that atoms interact is known: i ℏ ∂ Ψ ∂ t = H Ψ H ψ = E 0 ψ BigDFT and GPU Exploration of the configuration space Atomistic Simulations E pot DFT Ab initio codes BigDFT Properties BigDFT and GPUs Code details R1 BigDFT and HPC GPU Practical cases Discussion Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Atomistic Simulations Two intrinsic difficulties for numerical atomistic simulations, related to complexity: Interactions The way that atoms interact is known: i ℏ ∂ Ψ ∂ t = H Ψ H ψ = E 0 ψ BigDFT and GPU Exploration of the configuration space Atomistic Simulations E pot DFT Ab initio codes BigDFT Properties BigDFT and GPUs Code details R1 BigDFT and HPC GPU R2 Practical cases Discussion Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Atomistic Simulations Two intrinsic difficulties for numerical atomistic simulations, related to complexity: Interactions The way that atoms interact is known: i ℏ ∂ Ψ ∂ t = H Ψ H ψ = E 0 ψ BigDFT and GPU Exploration of the configuration space Atomistic Simulations E pot DFT Ab initio codes BigDFT Properties BigDFT and GPUs Code details R1 BigDFT and HPC GPU R3 R2 Practical cases Discussion Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Atomistic Simulations Two intrinsic difficulties for numerical atomistic simulations, related to complexity: Interactions The way that atoms interact is known: i ℏ ∂ Ψ ∂ t = H Ψ H ψ = E 0 ψ BigDFT and GPU Exploration of the configuration space Atomistic Simulations E pot DFT R1000 Ab initio codes BigDFT Properties BigDFT and GPUs Code details R1 BigDFT and HPC R41 GPU R3 R2 Practical cases Rn Discussion Messages Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Choice of Atomistic Methods 3 criteria G P 1 → Generality (elements, alloys) 2 → Precision ( ∆ r , ∆ E ) 3 → System size ( N , ∆ t ) S BigDFT and GPU Chemistry and Physics Atomistic Simulations DFT Force Fields Ab initio codes G P G P G P BigDFT Tight Binding Properties BigDFT and GPUs Hartree-Fock Code details S S S BigDFT and DFT HPC G P G P G P GPU Conf. Inter. Practical cases Discussion Quantum S S S Messages Monte-Carlo Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Choice of Atomistic Methods 3 criteria G P 1 → Generality (elements, alloys) 2 → Precision ( ∆ r , ∆ E ) 3 → System size ( N , ∆ t ) S BigDFT and GPU Chemistry and Physics Atomistic Simulations DFT Force Fields Ab initio codes G P G P G P BigDFT Tight Binding Properties BigDFT and GPUs Hartree-Fock Code details S S S BigDFT and DFT HPC G P G P G P GPU Conf. Inter. Practical cases Discussion Quantum S S S Messages Monte-Carlo Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Choice of Atomistic Methods 3 criteria G P 1 → Generality (elements, alloys) 2 → Precision ( ∆ r , ∆ E ) 3 → System size ( N , ∆ t ) S BigDFT and GPU Chemistry and Physics Atomistic Simulations DFT Force Fields Ab initio codes G P G P G P BigDFT Tight Binding Properties BigDFT and GPUs Hartree-Fock Code details S S S BigDFT and DFT HPC G P G P G P GPU Conf. Inter. Practical cases Discussion Quantum S S S Messages Monte-Carlo Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Choice of Atomistic Methods 3 criteria G P 1 → Generality (elements, alloys) 2 → Precision ( ∆ r , ∆ E ) 3 → System size ( N , ∆ t ) S BigDFT and GPU Chemistry and Physics Atomistic Simulations DFT Force Fields Ab initio codes G P G P G P BigDFT Tight Binding Properties BigDFT and GPUs Hartree-Fock Code details S S S BigDFT and DFT HPC G P G P G P GPU Conf. Inter. Practical cases Discussion Quantum S S S Messages Monte-Carlo Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Choice of Atomistic Methods 3 criteria G P 1 → Generality (elements, alloys) 2 → Precision ( ∆ r , ∆ E ) 3 → System size ( N , ∆ t ) S BigDFT and GPU Chemistry and Physics Atomistic Simulations DFT Force Fields Ab initio codes G P G P G P BigDFT Tight Binding Properties BigDFT and GPUs Hartree-Fock Code details S S S BigDFT and DFT HPC G P G P G P GPU Conf. Inter. Practical cases Discussion Quantum S S S Messages Monte-Carlo Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Choice of Atomistic Methods 3 criteria G P 1 → Generality (elements, alloys) 2 → Precision ( ∆ r , ∆ E ) 3 → System size ( N , ∆ t ) S BigDFT and GPU Chemistry and Physics Atomistic Simulations DFT Force Fields Ab initio codes G P G P G P BigDFT Tight Binding Properties BigDFT and GPUs Hartree-Fock Code details S S S BigDFT and DFT HPC G P G P G P GPU Conf. Inter. Practical cases Discussion Quantum S S S Messages Monte-Carlo Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
The Hohenberg-Kohn theorem A tremendous numerical problem N − 1 r i + V ext ( r i , { R } )+ 1 1 ∑ 2 ∇ 2 2 ∑ H = | r i − r j | i = 1 i � = j The Schrödinger is very difficult to solve for more than two BigDFT and electrons! Another approach is imperative GPU Atomistic The fundamental variable of the problem is however not the Simulations DFT wavefunction, but the electronic density Ab initio codes BigDFT � d r 2 ··· d r N ψ ∗ ( r , r 2 , ··· , r N ) ψ ( r , r 2 , ··· , r N ) ρ ( r ) = N Properties BigDFT and GPUs Code details Hohenberg-Kohn theorem (1964) BigDFT and HPC The ground state density ρ ( r ) of a many-electron system GPU Practical cases uniquely determines (up to a constant) the external potential . Discussion Messages The external potential is a functional of the density V ext = V ext [ ρ ] Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim Luigi Genovese
Recommend
More recommend
