A fast multipole formulation for 2D linear viscoelastic problems is presented in this paper by incorporating the elastic–viscoelastic correspondence principle. Systems of multipole expansion equations are formed and solved analytically in Laplace transform domain. Three commonly used viscoelastic models are introduced to characterize the time-dependent behavior of the materials. Since the trans...

In this paper the well-established minimal path framework is applied to the problem of computing blood flow trajectories in phase contrast magnetic resonance imaging (PC-MRI). The velocity vectors measured by PC-MRI and an uncertainty measure are combined to a metric tensor and minimal paths are calculated with anisotropic fast marching method (FMM). Exemplary results of the computation of the ...

A propagating interface can develop corners and discontinuities as it advances. Level set algorithms have been extensively applied for the problems in which the solution has advancing fronts. One of the most popular level set algorithms is the so called fast marching method (FMM), which requires total O(N log2N) operations, where N is the number of grid points. The article is concerned with the...

According to the Uniformization Theorem, any surface can be conformally mapped into a domain of a constant Gaussian curvature. The conformal factor indicates the local scaling introduced by such a mapping. This process could be used to compute geometric quantities in a simplified flat domain with zero Gaussian curvature. For example, the computation of geodesic distances on a curved surface can...