title: Numerical quadrature and operator splitting in finite element methods for cardiac electrophysiology.
abstract: We study the numerical accuracy and computational efficiency of alternative formulations of the finite element solution procedure for the monodomain equations of cardiac electrophysiology, focusing on the interaction of spatial quadrature implementations with operator splitting and examining both nodal and Gauss quadrature methods and implementations that mix nodal storage of state variables with Gauss quadrature. We evaluate the performance of all possible combinations of 'lumped' approximations of consistent capacitance and mass matrices. Most generally, we find that quadrature schemes and lumped approximations that produce decoupled nodal ionic equations allow for the greatest computational efficiency, this being afforded through the use of asynchronous adaptive time-stepping of the ionic state variable ODEs. We identify two lumped approximation schemes that exhibit superior accuracy, rivaling that of the most expensive variationally consistent implementations. Finally, we illustrate some of the physiological consequences of discretization error in electrophysiological simulation relevant to cardiac arrhythmia and fibrillation. These results suggest caution with the use of semi-automated free-form tetrahedral and hexahedral meshing algorithms available in most commercially available meshing software, which produce nonuniform meshes having a large distribution of element sizes.
authors.affiliation: Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA.
authors.forename: Shankarjee
authors.initials: S
authors.lastname: Krishnamoorthi
authors.forename: Mainak
authors.initials: M
authors.lastname: Sarkar
authors.forename: William S
authors.initials: WS
authors.lastname: Klug
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D022062:Electrophysiologic Techniques, Cardiac / Q000379:methods*; D020342:Finite Element Analysis; D006321:Heart / Q000502:physiology; D008955:Models, Cardiovascular
keywords: cardiac electrophysiology; finite element methods; operator splitting