Matrix-oriented numerical methods for semilinear PDEs

Abstract: The numerical solution of time dependent semilinear partial differential equations in two space dimensions typically leads to discretized problems of large size.
Under certain hypotheses on the physical domain, the space-discretized problem can be formulated as a matrix differential equation, with significant advantages in the computational costs, memory requirements and structure preservation. Moreover, time integrators can conveniently exploit this matrix framework.
To mitigate the difficulties associated with fine discretizations, proper orthogonal decompositions (POD) methodologies and discrete empirical interpolation (DEIM) strategies are commonly employed to reduce the problem dimensions. We propose a novel matrix-oriented POD/DEIM approach that allows us to apply matrix time integrators to the reduced differential problem.
These are joint works with Maria Chiara D'Autilia and Ivonne Sgura (Università del Salento), and Gerhard Kirsten (Università di Bologna).

numerical analysis

Audience: researchers in the topic

Seminars on Numerics and Applications