A deflated preconditioned conjugate gradient solver for electro-quasistatic finite element simulations

2011 ◽  
Author(s):  
D. Schmidthausler ◽  
M. Clemens
Keyword(s):  
Finite Element ◽  
Conjugate Gradient ◽  
Finite Element Simulations ◽  
Preconditioned Conjugate Gradient ◽  
Conjugate Gradient Solver

scholarly journals Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jianfei Zhang ◽  
Lei Zhang
Keyword(s):  
Finite Element ◽  
Conjugate Gradient ◽  
Preconditioned Conjugate Gradient ◽  
Polynomial Method ◽  
Processing Unit ◽  
Element Discretization ◽  
Mixed Precision ◽  
Element Computation ◽  
Finite Element Computation ◽  
Conjugate Gradient Solver

Graphics processing unit (GPU) has obtained great success in scientific computations for its tremendous computational horsepower and very high memory bandwidth. This paper discusses the efficient way to implement polynomial preconditioned conjugate gradient solver for the finite element computation of elasticity on NVIDIA GPUs using compute unified device architecture (CUDA). Sliced block ELLPACK (SBELL) format is introduced to store sparse matrix arising from finite element discretization of elasticity with fewer padding zeros than traditional ELLPACK-based formats. Polynomial preconditioning methods have been investigated both in convergence and running time. From the overall performance, the least-squares (L-S) polynomial method is chosen as a preconditioner in PCG solver to finite element equations derived from elasticity for its best results on different example meshes. In the PCG solver, mixed precision algorithm is used not only to reduce the overall computational, storage requirements and bandwidth but to make full use of the capacity of the GPU devices. With SBELL format and mixed precision algorithm, the GPU-based L-S preconditioned CG can get a speedup of about 7–9 to CPU-implementation.

Large-Scale Parallel Finite Element Analysis of the Stress Singular Problems

2002 ◽  
Author(s):  
Noriyuki Kushida ◽  
Hiroshi Okuda ◽  
Genki Yagawa
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Preconditioned Conjugate Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Singular Problems ◽  
Parallel Finite Element

In this paper, the convergence behavior of large-scale parallel finite element method for the stress singular problems was investigated. The convergence behavior of iterative solvers depends on the efficiency of the preconditioners. However, efficiency of preconditioners may be influenced by the domain decomposition that is necessary for parallel FEM. In this study the following results were obtained: Conjugate gradient method without preconditioning and the diagonal scaling preconditioned conjugate gradient method were not influenced by the domain decomposition as expected. symmetric successive over relaxation method preconditioned conjugate gradient method converged 6% faster as maximum if the stress singular area was contained in one sub-domain.

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