Visual Analysis of Convergence Process in Numerical Simulation and Its Application to Algorithm Optimization

Abstract

This paper reports a case study on the visual analysis for the development of a numerical computation algorithm. In order to accelerate the convergence speed of iterative numerical computation, the authors introduced a visual analysis of the convergence process into their algorithm design steps. In this visual analysis process, the authors discovered a phenomenon of the unnecessary divergence of residuals which may impede the speed of the convergence. Finally, this paper reports that their new algorithm which restricts the unnecessary divergence of residuals achieves reasonable acceleration of the performance for their surgical simulation.