Robust Solvers

Basic, flexible software components for creating PDE solvers constitute the focus of the Fluid Flow Components subproject in the Computational Middleware project. In the Robust Solvers project, such components are used to realize specific PDE solvers, which are used in the research on numerical methods to arrive at robust simulation tools for the complex physical problems targeted in the two application projects Biomedical Flows and Structure and Cardiac Computations. Primary examples are solvers for fluid flow and fluid-structure interaction, as well as solvers for propagation of electrical signals in the heart and coupling of such signals and the mechanical deformation of the heart tissue.

By "robust" we mean methods that improve convergence in nonlinear problems and provide (automatic) control of approximation errors. Improved convergence often implies increased implicitness, which complicates the implementation of compound solvers and calls for efficient methods for solving the associated linear algebra problems. Error control is achieved by employing adaptive finite element methodology.

The following subprojects are targeted:

• Adaptive FSI
• Implicit Coupling of Solvers
• Laboratory Experiments and Validation
• Particle Transport in Fluids
• Computability of Dynamical Systems