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arXiv · 1909.09771

Multithreaded Filtering Preconditioner for Diffusion Equation on Structured Grid

Abhinav Aggarwal·Shivam Kakkar·Pawan Kumar
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Abstract

A parallel and nested version of a frequency filtering preconditioner is proposed for linear systems corresponding to diffusion equation on a structured grid. The proposed preconditioner is found to be robust with respect to jumps in the diffusion coefficients. The storage requirement for the preconditioner is O(N),where N is number of rows of matrix, hence, a fairly large problem of size more than 42 million unknowns has been solved on a quad core machine with 64GB RAM. The parallelism is achieved using twisted factorization and SIMD operations. The preconditioner achieves a speedup of 3.3 times on a quad core processor clocked at 4.2 GHz, and compared to a well known algebraic multigrid method, it is significantly faster in both setup and solve times for diffusion equations with jumps.

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Abhinav Aggarwal, Shivam Kakkar, Pawan Kumar. 2021-09-20. Multithreaded Filtering Preconditioner for Diffusion Equation on Structured Grid. https://arxiv.org/abs/1909.09771

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