document: Myocardial electrical propagation can be simulated using the monodomain or bidomain PDEs [5,6]. Due to its capacity to represent complex geometries with ease, approximations are often obtained using the finite element method (FEM) to discretise the PDEs in space on realistic cardiac geometry meshes; this results in very large (up to forty-million degrees of freedom (DOF) for human heart geometries) systems of linear equations which must be solved many thousands of times over the course of even a short simulation. Thus, they are extremely computationally demanding, presenting taxing problems even to high-end supercomputing resources. This computational demand means that effort has been invested in developing efficient solution techniques, including work on preconditioning, parallelisation and adaptivity in space and time [7–12]. In this study, we investigate the potential of reducing the number of DOF by using a high-order polynomial FEM [13–15] to approximate the monodomain PDE in space, with the goal of significantly improving simulation efficiency over the piecewise-linear FEM approach commonly used in the field [16–19]. For schemes where the polynomial degree p of the elements is adjusted according to the error in the approximation, this is known as the finite element p-version. In the work presented here, we work with schemes which keep p fixed.
doc_bio_tags: B I I O O O O O B I I I O O O O O O O O B O O O O O O O O B I I B O O O B O O O O B I I O O O O O O O O O O O O O O O B B I I I O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O B B O B I I I I O O O O O B I I I I I I I I O O O O O B O O O O B I O O O O O O B I I I O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: adaptivity in space and time cardiac geometry meshes developing efficient solution techniques fem finite element method geometries investigate the potential of reducing the number of dof monodomain or bidomain pdes monodomain pde myocardial electrical propagation parallelisation pdes preconditioning significantly improving simulation efficiency simulation systems of linear equations
abstractive_keyphrases: finite element p-version high-end supercomputing resources high-order polynomial fem human heart geometries piecewise-linear fem simulation efficiency