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arXiv · 2408.14926

Fast numerical solvers for parameter identification problems in mathematical biology

Karolína Benková·John W. Pearson·Mariya Ptashnyk
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Abstract

In this paper, we consider effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization models for 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.

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Karolína Benková, John W. Pearson, Mariya Ptashnyk. 2024-08-27. Fast numerical solvers for parameter identification problems in mathematical biology. https://arxiv.org/abs/2408.14926

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