GPU Accelerated Implicit Kinetic Meshfree Method based on Modified LU-SGS

TL;DR

This paper introduces a GPU-accelerated implicit kinetic meshfree method using a modified LU-SGS algorithm with exact Jacobian vector products via algorithmic differentiation, improving efficiency and convergence.

Contribution

It presents a novel GPU-accelerated implicit kinetic meshfree method with exact Jacobian computation, enhancing performance over approximate methods.

Findings

GPU solvers with exact Jacobian computation are more efficient.

Exact Jacobian computation improves convergence rates.

Benchmarks show superior performance of the proposed method.

Abstract

This report presents the GPU acceleration of implicit kinetic meshfree methods using modified LU-SGS algorithms. The meshfree scheme is based on the least squares kinetic upwind method (LSKUM). In the existing matrix-free LU-SGS approaches for kinetic meshfree methods, the products of split flux Jacobians and increments in conserved vectors are approximated by increments in the split fluxes. In our modified LU-SGS approach, the Jacobian vector products are computed exactly using algorithmic differentiation (AD). The implicit GPU solvers with exact and approximate computation of the Jacobian vector products are applied to the standard test cases for two-dimensional inviscid flows. Numerical results have shown that the GPU solvers with the exact computation of the Jacobian vector products are computationally more efficient and yield better convergence rates than the solvers with approximations to the Jacobian vector products. Benchmarks are presented to assess the performance of implicit GPU solvers compared to the explicit GPU solver and the implicit serial LSKUM solver.