John N. Shadid

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Spontaneously generated calcium (Ca2+) waves can trigger arrhythmias in ventricular and atrial myocytes. Yet, Ca2+ waves also serve the physiological function of mediating global Ca2+ increase and muscle contraction in atrial myocytes. We examine the factors that influence Ca2+ wave initiation by mathematical modeling and large-scale computational(More)
This paper introduces a strategy for automatically generating a block preconditioner for solving the incompressible Navier–Stokes equations. We consider the “pressure convection– diffusion preconditioners” proposed by Kay, Loghin, and Wathen [11] and Silvester, Elman, Kay, and Wathen [16]. Numerous theoretical and numerical studies have demonstrated mesh(More)
In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier–Stokes equations based on preconditioned Krylov methods. These include physicsbased methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques(More)
The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript we focus on evaluating a proposed(More)
In this paper, we analyze a multiscale operator splitting method for solving systems of ordinary differential equations such as those that result upon space discretization of a reactiondiffusion equation. Our goal is to analyze and accurately estimate the error of the numerical solution, including the effects of any instabilities that can result from(More)
We consider multiphysics applications from algorithmic and architectural perspectives, where ‘‘algorithmic’’ includes both mathematical analysis and computational complexity, and ‘‘architectural’’ includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common(More)
This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The(More)
Stability analysis algorithms coupled with a robust Newton-Krylov steady state iterative solver are used to understand the behavior of the 2D model problem of thermal convection in a 8:1 differentially heated cavity. Parameter continuation methods along with bifurcation and linear stability analysis are used to study transition from steady to transient flow(More)
We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm,(More)
In this paper we describe general software utilities for performing unstructured sparse matrix-vector multiplications on distributed-memory message-passing computers. The matrix-vector multiply comprises an important kernel in the solution of large sparse linear systems by iterative methods. Our focus is to present the data structures and communication(More)