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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月1日

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  • Derese Wendimu Ayitaged,
  • Tamirat Temesgen Dufera,
  • Mesfin Mekuria Woldaregay

摘要

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.