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<p>In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models of pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization of the optimization problem, we devise appropriate time-stepping schemes and discrete approximations of the cost functionals such that the discretization and optimization operations are commutative, a highly desirable property of a discretization of such problems. We formulate the large-scale, coupled linear systems in such a way that efficient preconditioned iterative methods can be applied within a Krylov subspace solver. Numerical experiments demonstrate the viability and efficiency of our approach.</p>

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Fast Numerical Solvers for Parameter Identification Problems in Mathematical Biology

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月16日

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  • Karolína Benková,
  • John W. Pearson,
  • Mariya Ptashnyk

摘要

In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models of pattern evolution within biological processes. Upon a Sequential Quadratic Programming linearization of the optimization problem, we devise appropriate time-stepping schemes and discrete approximations of the cost functionals such that the discretization and optimization operations are commutative, a highly desirable property of a discretization of such problems. We formulate the large-scale, coupled linear systems in such a way that efficient preconditioned iterative methods can be applied within a Krylov subspace solver. Numerical experiments demonstrate the viability and efficiency of our approach.