A multigrid Waveform Relaxation Method for solving the Pennes bioheat equation

Abstract

This work proposes a multigrid Waveform Relaxation Method (WRMG) that uses the finite difference method for the discretization to solve Pennes’ bioheat equation. There is no evidence in the literature of using the WRMG to solve this equation. The proposed algorithm is based on the red-black Gauss-Seidel smoother in space and the line Gauss-Seidel smoother in time. Verification of code is presented. The performance analysis of the multigrid method confirms the convergence and efficiency of the algorithm. The method, which favors parallel architecture, is tested in two-dimensional numerical experiments on an academic problem and for the thermal analysis of human skin.

Keywords:

• Bioheat equation
• multigrid
• parallel architecture
• Waveform Relaxation

SUBJECT CLASSIFICATION CODES:

• 65B99
• 65F10
• 65N22
• 65M55

Acknowledgments

The authors acknowledge the Coordination for the Improvement of Higher Education Personnel (CAPES), Brazil, the LAMAP-AP of the Federal Technological University of Paraná (UTFPR), and Federal University of Paraná (UFPR).

Disclosure statement

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.