The numerical solution of Helmholtz’ equation at large wavenumber is very expensive if attempted by ”traditional” discretisation methods (FDM, standard Galerkin FEM). For reliable results, the mesh has to be very fine. The bad performance of the traditional FEM for Helmholtz problems can be related to the deterioration of stability of the Helmholtz differential operator at high wavenumber. As a...

BACKGROUND The finite element method (FEM) has been used to simulate cardiac and hepatic radiofrequency (RF) ablation. The FEM allows modeling of complex geometries that cannot be solved by analytical methods or finite difference models. In both hepatic and cardiac RF ablation a common control mode is temperature-controlled mode. Commercial FEM packages don't support automating temperature cont...

In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engw...

Abstract. We describe our investigation of a fast 3D finite element method (FEM) for biomedical simulation of a muscle-activated human tongue. Our method uses a linear stiffness-warping scheme to achieve simulation speeds which are within a factor 10 of real-time rates at the expense of a small loss in accuracy. Muscle activations are produced by an arrangement of forces acting along selected e...

Chloride-induced corrosion is a key factor in the premature corrosion of concrete structures exposed to a marine environment. Fick's second law of diffusion is the dominant equation to model diffusion of chloride ions. This equation is traditionally solved by Finite Element Method (FEM) and Finite Difference Method (FDM). Although these methods are robust and efficient, they may face some numer...

The solution of a linear reaction diffusion equation on a non-convex polygon is proved to be globally regular in a suitable weighted Sobolev space. This result is used to design an optimally convergent Fourier-Finite Element Method (FEM) where the mesh size is suitably refined. Furthermore, the coupled Non-Standard Finite Difference Method (NSFDM)-FEM is presented as a reliable scheme that repl...

When solving numerically the stiff second order ODE system obtained after semidiscretizing the wave-type partial differential equation (PDE) with the finite element method (FEM), and similarly to the HHTα method, which allows the numerical damping of the undesirable high frequency modes associated to FEM semidiscretization, we have constructed a modification of the 2-order BDF method (the BDF2 ...

The method of auxiliary mapping (MAM) introduced by Babu ska-Oh((10]) was eecient and successful in dealing with plane elliptic boundary value problems containing singularities. In this paper, MAM is generalized for elliptic PDEs on non-smooth domains in R 3 : This method is tested in the framework of the p-version of the nite element method (FEM) for the axisymmetric Poisson equations containi...

We describe our investigation of a fast 3D finite element method (FEM) for biomedical simulation of a muscle-activated human tongue. Our method uses a linear stiffness-warping scheme to achieve simulation speeds which are within a factor 10 of real-time rates at the expense of a small loss in accuracy. Muscle activations are produced by an arrangement of forces acting along selected edges of th...