Performance Evaluation of Iterative Solvers for Vectorized Quasi-Static Heat Conduction in Peridynamics

Heat conduction analyses on discontinuities via Peridynamics require a large amount of calculations.In this study, we propose a vectorization process to solve the peridynamic governing equations for quasi-static heat conduction analyses and suggest the optimal iterative solver.The heat equation is expressed by using peridynamic differential operators, and simplified for thermally isotropic simulations.The governing equation represented with compressed sparse row matrices consists of an off-diagonal sparse matrix and two diagonal matrices.Using vectorized operations, these matrices are further split into matrices related to the geometry.Four iterative solvers such as BiCG, BiCGSTAB, GMRES, and LGMRES are applied to solve the vectorized equation, and LGMRES demonstrates the best convergence times with the least number of calculation steps for several types of geometries.The temperature fields yielded by LGMRES are in good agreement with the results by the finite element analyses in the quasi-static thermal condition.This proposed vectorization procedure and the optimized iterative solver on Peridynamics will be useful to simulate the fully coupled thermomechanics.