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Fast Numerical Solvers for Parameter Identification Problems in Mathematical Biology
Karolína Benková1, John W Pearson2, Mariya Ptashnyk3
1The Bayes Centre, The Maxwell Institute for Mathematical Sciences, 47 Potterrow, Edinburgh, EH8 9BT Scotland, UK.
None:
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.
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