We are happy to announce the following JRF to SRF talk.
Speaker: Himani Roul (IISER TVM)
Date & time: 18th July, (Friday) 2025 & 2.30pm
Venue: PSB1207
Title: Analysis of Sparse Optimization in the Monodomain Model with Gradient-Type Cost Functional
Abstract: This work explores the sparse optimal control problem combined with the gradient-type terms arising from the monodomain model in cardiac electrophysiology. The objective functional consists of a standard quadratic tracking term, the L^2 norm of the gradient of the state variable, and a sparsity-promoting term based on the L^1 norm. The inclusion of the gradient term introduces a Laplacian term in the adjoint system, which requires higher regularity for the state variable to ensure the well-posedness of the system. We establish the existence of the adjoint equations and derive the first- and second-order optimality conditions. Numerical results demonstrate that placing greater emphasis on the L^1 term in the cost functional enlarges the sparsity region, indicating that the optimal control becomes zero over a broader area of the domain. Additionally, the inclusion of the gradient term accelerates the decay of the excitation wave towards the desired state. The proposed optimal control problem is solved using the semi-smooth Newton method, with numerical results exhibiting superlinear convergence in agreement with theoretical predictions.