Adaptive Wavelet-Galerkin Modelling of Heat Conduction in Heterogeneous Composite Materials

TL;DR

This paper introduces an adaptive wavelet Galerkin method for simulating heat conduction in heterogeneous composites, efficiently capturing sharp gradients with fewer degrees of freedom.

Contribution

It combines multiresolution wavelet bases with adaptive refinement to improve computational efficiency in modeling heat transfer in complex materials.

Findings

Accurately resolves sharp temperature gradients near interfaces.

Reduces degrees of freedom compared to uniform methods.

Demonstrates efficiency in layered and graded composites.

Abstract

We present an adaptive wavelet Galerkin method for transient heat conduction in heterogeneous composite materials. The approach combines multiresolution wavelet bases with an implicit time discretization to efficiently resolve sharp temperature gradients near material interfaces and boundary layers. Adaptive refinement is driven by wavelet coefficients, significantly reducing the number of degrees of freedom compared to uniform discretizations. Numerical examples demonstrate accurate resolution of layered, inclusion-based, and functionally graded composites with improved computational efficiency.