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Very Weak Space-Time Variational Formulation for the Wave Equation: Analysis and Efficient Numerical Solution
Julian Henning, Davide Palitta, Valeria Simoncini +1
We introduce a very weak space-time variational formulation for the wave equation, prove its well-posedness (even in the case of minimal regularity) and optimal inf-sup stability.…
A low-rank matrix equation method for solving PDE-constrained optimization problems
Alexandra Bünger, Valeria Simoncini, Martin Stoll
PDE-constrained optimization problems arise in a broad number of applications such as hyperthermia cancer treatment or blood flow simulation. Discretization of the optimization pro…
Matrix oriented reduction of space-time Petrov-Galerkin variational problems
Julian Henning, Davide Palitta, Valeria Simoncini +1
Variational formulations of time-dependent PDEs in space and time yield -dimensional problems to be solved numerically. This increases the number of unknowns as well as the…
Optimality properties of Galerkin and Petrov-Galerkin methods for linear matrix equations
Davide Palitta, Valeria Simoncini
Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their…
Order reduction methods for solving large-scale differential matrix Riccati equations
Gerhard Kirsten, Valeria Simoncini
We consider the numerical solution of large-scale symmetric differential matrix Riccati equations. Under certain hypotheses on the data, reduced order methods have recently arisen…