Time-domain boundary integral equation modeling of heat transmission problems
Provides improved numerical analysis for heat transmission modeling, but the improvement is incremental for a specific domain.
The paper develops a convolution quadrature boundary element method for time-dependent heat transmission problems, achieving better error estimates than the traditional Laplace domain approach.
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical scheme. Semigroup theory is applied to obtain stability in spatial semidiscrete scheme. Functional calculus is employed to yield convergence in the fully discrete scheme. In comparison to the traditional Laplace domain approach, we show our approach gives better estimates.