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In this work, we developed a parallelizable algorithm combining an overlapping Schwarz method (OS) with space compact finite difference and time Crank-Nicolson scheme (CFD) to approximate the Euler-Bernoulli beam equation with variable coefficients. First we study the compact finite difference method applied to our problem. Next, we give the description of the overlapping Schwarz algorithm in the continuous and discrete forms, where the subproblems are discretized using the CFD method. The resulting new algorithm will be denoted OS-CFD. After that, numerical examples are presented to support the theoretical results of CFD and to study the properties of OS-CFD. The obtained numerical results are satisfactory.

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A New Algorithm Coupling Schwarz Domain Decomposition and High-Order Compact Finite Difference to Solve an Euler-Bernoulli Beam Equation with Variable Coefficients

  • 会议论文

  • 发表日期：

    2025年

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  • Abdelhalim Ben bouzid,
  • Yassin Khali,
  • Samir Khallouq

摘要

In this work, we developed a parallelizable algorithm combining an overlapping Schwarz method (OS) with space compact finite difference and time Crank-Nicolson scheme (CFD) to approximate the Euler-Bernoulli beam equation with variable coefficients. First we study the compact finite difference method applied to our problem. Next, we give the description of the overlapping Schwarz algorithm in the continuous and discrete forms, where the subproblems are discretized using the CFD method. The resulting new algorithm will be denoted OS-CFD. After that, numerical examples are presented to support the theoretical results of CFD and to study the properties of OS-CFD. The obtained numerical results are satisfactory.