Fast numerical solvers for parameter identification problems in mathematical biology
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912002903900160 |
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| author | Benková, Karolína Pearson, John W. Ptashnyk, Mariya |
| author_facet | Benková, Karolína Pearson, John W. Ptashnyk, Mariya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fast numerical solvers for parameter identification problems in mathematical biology Benková, Karolína Pearson, John W. Ptashnyk, Mariya Numerical Analysis Optimization and Control 49M41, 92C15, 65M22, 65M60, 65F08, 65F10 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. |
| title | Fast numerical solvers for parameter identification problems in mathematical biology |
| topic | Numerical Analysis Optimization and Control 49M41, 92C15, 65M22, 65M60, 65F08, 65F10 |
| url | https://arxiv.org/abs/2408.14926 |