A pseudo-spectral scheme for the incompressible Navier-Stokes equations using unstructured nodal elements

A pseudo-spectral scheme for solving the incompressible Navier-Stokes equations using unstructured nodal triangles is proposed. Efficient algorithms are developed with numerical evidence that indicates optimal rates of convergence can be achieved. Navier-Stokes simulations of Kovasznay, shear layer roll up, and Row past a cylinder are included to show comparisons between the different nodal sets considered and an alternative modal approach. (C) 2000 Academic Press

Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes

In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp-version symmetric interior penalty discontinuous Galerkin discretizations of second-order elliptic partial differential equations on polygonal/polyhedral meshes. We prove that the two-level method converges uniformly with respect to the granularity of the grid and the polynomial approximation degree p, provided that the number of smoothing steps, which depends on p, is chosen sufficiently large. An analogous result is obtained for the W-cycle multigrid algorithm, which is proved to be uniformly convergent with respect to the mesh size, the polynomial approximation degree, and the number of levels, provided the latter remains bounded and the number of smoothing steps is chosen sufficiently large. Numerical experiments are presented which underpin the theoretical predictions; moreover, the proposed multilevel solvers are shown to be convergent in practice, even when some of the theoretical assumptions are not fully satisfied

A comparative study of scalable multilevel preconditioners for cardiac mechanics

In this work, we provide a performance comparison between the Balancing Domain Decomposition by Constraints (BDDC) and the Algebraic Multigrid (AMG) preconditioners for cardiac mechanics on both structured and unstructured finite element meshes. The mechanical behavior of myocardium can be described by the equations of threedimensional finite elasticity, which are discretized by finite elements in space and yield the solution of a large scale nonlinear algebraic system. This problem is solved by a Newton-Krylov method, where the solution of the Jacobian linear system is accelerated by BDDC/AMG preconditioners. We thoroughly explore the main parameters of the BDDC preconditioner in order to make the comparison fair. We focus on: the performance of different direct solvers for the local and coarse problems of the BDDC algorithm; the impact of the different choices of BDDC primal degrees of freedom; and the influence of the finite element degree. Scalability tests are performed on Linux clusters up to 1024 processors, and we conclude with a performance study on a realistic electromechanical simulation.& COPY; 2023 Elsevier Inc. All rights reserved

Performance evaluation of cardiac repolarization markers derived from monophasic action potentials and unipolar electrograms: a simulation study

Performance evaluation of cardiac repolarization markers derived from monophasic action potentials and unipolar electrograms using 3-dimensional parallel simulations of the bidomain models of the cardiac biolectric actitvitie

Modeling ventricular repolarization: effects of transmural and apex-to-base heterogeneities in action potential durations

Advanced multiscale models in computational electrocardiology offer a detailed representation of the heart bioelectrical activity, ranging from the microscopic description of ion channels of the cellular membrane to the macroscopic properties of anisotropic front propagation in the whole heart. Our model consists of a Monodomain or Bidomain tissue representation that includes orthotropic anisotropy, transmural fiber rotation and homogeneous or heterogeneous intrinsic membrane properties, described by Luo-Rudy type models. We consider membrane heterogeneities due either to the presence of midwall cells (M-cells) with different action potential durations (APDs) or to the presence of subendocardial ischemic regions. We present the results of large-scale simulations of an entire heartbeat with epicardial or endocardial pacing of three-dimensional ventricular blocks. We will also discuss some numerical features of our simulations, including parallel scalability, multilevel preconditioning and space-time adaptivity