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SUMMARY The material point method (MPM) has demonstrated itself as a computationally effective particle method for solving solid mechanics problems involving large deformations and/or fragmentation of structures, which are sometimes problematic for finite element methods (FEMs). However, similar to most methods that employ mixed Lagrangian (particle) and… (More)

- E Cohen, T Martin, R M Kirby, T Lyche, R F Riesenfeld
- 2010

Keywords: Isogeometric analysis Solid modeling Mesh generation Mesh quality Model generation Model quality a b s t r a c t Isogeometric analysis has been proposed as a methodology for bridging the gap between computer aided design (CAD) and finite element analysis (FEA). Although both the traditional and isogeometric pipelines rely upon the same… (More)

- S J Sherwin, R M Kirby, J Peiró, R L Taylor, O C Zienkiewicz
- 2005

SUMMARY We discuss the discretization using discontinuous Galerkin (DG) formulation of an elliptic Poisson problem. Two commonly used DG schemes are investigated: the original average flux proposed by Bassi and Rebay (J. by adopting a matrix based notation with a view to highlighting the steps required in a numerical implementation of the DG method. Through… (More)

By combining a static bidomain heart model with a torso conduction model, we studied the inverse electrocardiographic problem of computing the transmembrane potentials (TMPs) throughout the myocardium from a body-surface potential map, and then used the recovered potentials to localize myocardial ischemia. Our main contribution is solving the inverse… (More)

We present inspect, a tool for model checking safety properties of multithreaded C/C++ programs where threads interact through shared variables and synchronization primitives. The given program is mechanically transformed into an instrumented version that yields control to a centralized scheduler around each such interaction. The sched-uler first enables an… (More)

- Ross Whitaker, Robert M Kirby, Zhisong Fu
- 2010

This paper presents a method for computing thin layers of high-quality, triangular prisms that conform to surfaces that are specified as level sets of an implicit function. Triangular prisms are important in circumstances where vol-umetric meshes need to capture the geometries materials with thin layers–i.e. that are smooth relative to their thickness–or… (More)

- C D Cantwell, S J Sherwin, R M Kirby, P H J Kelly
- 2011

A spectral/hp element discretisation permits both geometric flexibility and beneficial convergence properties to be attained simultaneously. The choice of elemental polynomial order has a profound effect on the efficiency of different implementation strategies with their performance varying substantially for low and high order spectral/hp discretisations.… (More)

Markovian models of ion channels have proven useful in the reconstruction of experimental data and prediction of cellular electrophysiology. We present the stochastic Galerkin method as an alternative to Monte Carlo and other stochastic methods for assessing the impact of uncertain rate coefficients on the predictions of Markovian ion channel models. We… (More)

We present de-aliasing rules to be used when evaluating non-linear terms with polynomial spectral methods on non-uniform grids analogous to the de-aliasing rules used in Fourier spectral methods. They are based upon the idea of super-collocation followed by a Galerkin projection of the non-linear terms. We demonstrate through numerical simulation that both… (More)

- Elijah P Newren, Aaron L Fogelson, Robert D Guy, Robert M Kirby, P Newren, A L Fogelson +2 others
- 2007

Explicit time discretizations of the Immersed Boundary method are known to require small timesteps to maintain stability. A number of implicit methods have been introduced to alleviate this restriction to allow for a more efficient method, but many of these methods still have a stability restriction on the timestep. Furthermore , almost no comparisons have… (More)