The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and eve...

We are interested in the design of efficient geometric multigrid methods on hierarchical triangular grids for problems in two dimensions. Fourier analysis is a well-known useful tool in multigrid for the prediction of two-grid convergence rates which has been used mainly for rectangular–grids. This analysis can be extended straightforwardly to triangular grids by using an appropriate expression...

it is well-known that dam-reservoir interaction has significant effects on the response of dams to the earthquakes. this phenomenon should be considered more exactly in the seismic design of dams with a rational and reliable dynamic analysis method. in this research, seismic analysis of the dam-reservoir is studied as a wave propagation problem by using legendre spectral element method (sem). t...

A new agglomeration multigrid method is proposed in this paper for general unstructured grids. By a proper local agglomeration of finite elements, a nested sequence of finite dimensional subspaces are obtained by taking appropriate linear combinations of the basis functions from previous level of space. Our algorithm seems to be able to solve, for example, the Poisson equation discretized on an...

In this paper the buckling coefficient of FGM rectangular plates calculated by the new version of differential quadrature method (DQM). At the first the governing differential equation for plate has been calculated and then according to the new version of differential quadrature method (DQM) the existence derivatives in equation , convert to the amounts of function in the grid points inside of ...

This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the Euler equations. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximati...

We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed ...

Localization and quantification of the light sources generated by the expression of bioluminescent reporter genes is an important task in bioluminescent imaging of small animals, especially the generically engineered mice. To employ the Monte Carlo method for the light-source identification, the surfaces that define the anatomic structures of the small experimental animal is required; to perfor...

Bidomain models are commonly used for studying and simulating electrophysiological waves in the cardiac tissue. Most of the time, the associated PDEs are solved using explicit finite difference methods on structured grids. We propose an implicit finite element method using unstructured grids for an anisotropic bidomain model. The impact and numerical requirements of unstructured grid methods is...