# Multithreaded Filtering Preconditioner for Diffusion Equation on Structured Grid

arXiv: https://arxiv.org/abs/1909.09771 · HTML: https://mlsanity.com/paper/1909.09771/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Nonnegative Low-Rank Tensor Completion via Dual Formulation with Applications to Image and Video Completion](https://mlsanity.com/paper/2305.07976/) (2023)
- [Structured Low-Rank Tensor Learning](https://mlsanity.com/paper/2305.07967/) (2023)

## Abstract (arXiv)

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.