Space-time boundary domain integral equation approach for transient heat conduction governed by variable coefficients

Abstract

This work introduces a boundary-only integral formulation that couples the precise integration method with a parametrix-based approach to solve non-homogeneous transient heat conduction problems with space- and time-dependent coefficients. Using either the Laplace fundamental solution or a tailored parametrix (Levi function), the problem is recast as a boundary-domain integral equation. Domain integrals are eliminated via the radial integration method, yielding purely boundary-integral or boundary-integro-differential formulations. The resulting ODE system is solved efficiently using the precise integration method, while domain decomposition produces a sparse linear system, reducing computational cost. Numerical examples with known analytical solutions confirm the method’s accuracy and efficiency. A boundary integral method combines parametrix modeling with precise integration to solve transient heat conduction with space and time-varying properties. Radial integration method, augmented with radial basis functions, eliminates domain integrals by converting them into boundary-only integral equations. The technique reduces computational costs while preserving accuracy confirmed by analytical solutions by using domain decomposition to create a sparse linear system.