After a quarter century of development finite element methods have reached that point of maturity at which nobody doubts their effectiveness and power to solve various kinds of engineering problems with a variety of aspects, both very theoretical and extremely practical. Based on the construction of theories of finite element methods duri,ng the 396Os, many general-purpose codes have been devel...

Variational multiscale methods lead to stable finite element approximations of the Navier-Stokes equations, both dealing with the indefinite nature of the system (pressure stability) and the velocity stability loss for high Reynolds numbers. These methods enrich the Galerkin formulation with a sub-grid component that is modeled. In fact, the effect of the sub-grid scale on the captured scales h...

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor-grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can b...

High Reynolds number turbulent flows of incompressible fluids in plane channels and annuli are simulated using a finite difference procedure which integrates the NavierStokes equations in time and in three-dimensional space. This paper describes the finite difference procedure and the subgrid scale (SGS) motion model. The model differs from earlier ones in the following points. The finite diffe...

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

The finite difference time domain (FDTD) method has direct applications in musical instrument modeling, simulation of environmental acoustics, room acoustics and sound reproduction paradigms, all of which benefit from auralization. However, rendering binaural impulse responses from simulated data is not straightforward to accomplish as the calculated pressure at FDTD grid nodes does not contain...

Abstract. The interior of the Earth is heterogeneous with different material and may have complex geometry. The free surface can also be uneven. Therefore, the use of a meshless method with the possibility of using and irregular grid-point distribution can be interest for modelling this kind of problem. This paper shows the application of Generalized Finite Difference Method (GFDM) to the probl...

A triangular grid graph is a finite induced subgraph of the infinite graph associated with the two-dimensional triangular grid. We show that the problem Hamiltonian Cycle is NP-complete for triangular grid graphs, while a hamiltonian cycle in connected, locally connected triangular grid graph can be found in polynomial time. 2000 Mathematics Subject Classification: 05C38 (05C45, 68Q25).

A three dimensional hydrostatic finite volume ocean model has been developed to solve the integral dynamical equations. Since the basic (integral) equations are solved for finite volumes rather than grid points, the flux conservation is easily enforced, even on arbitrary meshes. Both upwind and high-order combined compact schemes can be incorporated into the model to increase computational stab...