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In this paper, we present an innovative numerical approach, incorporating the Scalar Auxiliary Variable (SAV) method, for efficiently solving a challenging multiscale diffuse interface model describing tumor growth within host tissue. Our approach employs a stabilized linear scheme, achieving second-order accuracy in both time and space through a modification of the Crank-Nicolson scheme for temporal discretization and employs the quadratic Lagrange finite element method for spatial discretization. The results of the numerical simulations validate the effectiveness of this approach by accurately reproducing complex tumor progression, highlighting the importance of using advanced numerical techniques, in particular the SAV approach, to model complex biological phenomena.

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Numerical Approximation for a Solid Tumor Growth Model

  • 会议论文

  • 发表日期：

    2025年

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  • Sonia Seyed Allaei,
  • Adélia Sequeira

摘要

In this paper, we present an innovative numerical approach, incorporating the Scalar Auxiliary Variable (SAV) method, for efficiently solving a challenging multiscale diffuse interface model describing tumor growth within host tissue. Our approach employs a stabilized linear scheme, achieving second-order accuracy in both time and space through a modification of the Crank-Nicolson scheme for temporal discretization and employs the quadratic Lagrange finite element method for spatial discretization. The results of the numerical simulations validate the effectiveness of this approach by accurately reproducing complex tumor progression, highlighting the importance of using advanced numerical techniques, in particular the SAV approach, to model complex biological phenomena.