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<p>A method for the efficient study and solution of conditionally well-posed elliptic problems with a unique solution in a subspace is developed. A three-stage regularization method is proposed to find a normal pseudosolution with guaranteed accuracy for a discrete problem, specifically a system of linear algebraic equations with a sparse symmetric semi-definite matrix. Parallel algorithms for solving systems of linear equations with symmetric block-sparse matrices are developed.</p>

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Solving Ill-Posed Elliptic Problems of Theory of Elasticity

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • O. M. Khimich,
  • A. V. Popov

摘要

A method for the efficient study and solution of conditionally well-posed elliptic problems with a unique solution in a subspace is developed. A three-stage regularization method is proposed to find a normal pseudosolution with guaranteed accuracy for a discrete problem, specifically a system of linear algebraic equations with a sparse symmetric semi-definite matrix. Parallel algorithms for solving systems of linear equations with symmetric block-sparse matrices are developed.