Architecting the Finite Element Method Pipeline for the GPU.

Area of Science:

• Computational Science and Engineering
• Numerical Analysis
• High-Performance Computing

Background:

• The finite element method (FEM) is crucial for solving partial differential equations (PDEs) across science and engineering.
• Accelerating the FEM pipeline is essential for computationally intensive applications.
• Modern hardware, like Graphics Processing Units (GPUs), offers potential for significant performance gains.

Purpose of the Study:

• To develop and present algorithms and data structures for executing the entire FEM pipeline on a GPU.
• To enable faster solutions for PDEs using FEM on massively parallel architectures.

Main Methods:

• An efficient GPU-based algorithm for local element information generation and global linear system assembly.
• Implementation of a conjugate gradient method with an algebraic multi-grid (AMG) preconditioner for solving linear systems on the GPU.
• A novel fine-grained parallelism strategy, multigrid cycling, and data mapping optimized for GPU architecture.

Main Results:

• Achieved up to an 87x speedup for on-GPU assembly compared to serial CPU implementation.
• Demonstrated up to a 51x speedup for the GPU-based linear system solver versus state-of-the-art serial CPU solvers.
• The proposed GPU-based FEM pipeline shows favorable performance compared to existing GPU sparse linear solvers.

Conclusions:

• The entire FEM pipeline can be effectively implemented on GPUs, leading to substantial performance improvements.
• The developed GPU algorithms and data structures significantly accelerate FEM computations, particularly for elliptic PDEs.
• This work paves the way for more efficient and faster simulations in various scientific and engineering domains utilizing GPUs.