3 research outputs found
ISOGEOMETRIC OVERLAPPING ADDITIVE SCHWARZ PRECONDITIONERS IN COMPUTATIONAL ELECTROCARDIOLOGY
In this thesis we present and study overlapping additive Schwarz preconditioner for
the isogeometric discretization of reaction-diffusion systems
modeling the heart bioelectrical activity, known as the Bidomain and
Monodomain models. The cardiac Bidomain model consists of a
degenerate system of parabolic and elliptic PDE, whereas the
simplified Monodomain model consists of a single parabolic
equation. These models include intramural fiber rotation,
anisotropic conductivity coefficients and are coupled through the
reaction term with a system of ODEs, which models the ionic currents
of the cellular membrane. The overlapping Schwarz preconditioner is
applied with a PCG accelerator to solve the linear system arising at
each time step from the isogeometric discretization in space and a
semi-implicit adaptive method in time. A theoretical convergence
rate analysis shows that the resulting solver is scalable, optimal
in the ratio of subdomain/element size and the convergence rate
improves with increasing overlap size. Numerical tests in
three-dimensional ellipsoidal domains confirm the theoretical
estimates and additionally show the robustness with respect to jump
discontinuities of the orthotropic conductivity coefficients