The remaining smooth portions of the mesh are refined using previously developed techniques. The method is demonstrated on two examples, and results indicate that the method solves optimal control problems with
The box method is applied to these problems and some results concerning the numerical treatment of interface singularities by appropriate local mesh refinement are presented. For triangular meshes with grading, basic inequalities for norms of grid functions on such meshes and some analytic and matrix ...
The scalability of Xcompact3D has been tested recently on various Tier-1/0 supercomputers ARCHER, MareNostrum and Hazel Hen with simulation sizes of more than 68 billion mesh nodes. The scalability plots have been obtained for the Taylor–Green case (see details in the next section) with a ...
orelements, over which it is possible to write a set of equations describing the solution to the governing equation. The mesh is also used to represent the solution field to the physics being solved. There is error associated with both the discretization of the ...
A novel meshless numerical procedure based on the method of fundamental solutions (MFS) is proposed to solve the primitive variables formulation of the Navier–Stokes equations. The MFS is a meshless method since it is free from the mesh generation and numerical integration. We will transform the...
Software Development Resources for Data Scientists Data scientists concentrate on making sense of data through exploratory analysis, statistics, and models. Software developers apply a separate set of knowledge with different tools. Although their focus may seem unrelated, data science teams can benefit ...
We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The embedded boundary of the domain is allowed to cut through the background mesh arbitrarily. The unfitted scheme is based on a mixed interior penalty formulation, where the...
Finally, to evaluate the L2 norm difference, we use the Surface Integration like in the case of a single parameter sweep. The difference here is that instead of using all solutions, we only use the case withhflux=8 W/(m2K)and all values of the mesh size. There can be reasons where ...
Numerical Solutions of a Class of Second Order Boundary Value Problems with Robin conditions A novel numerical approach, based on manipulating Green's function and fixed point iteration formula of Krasnoselskii-Mann, is presented. The method is app... M Abushammala,H Kafri - International Conferenc...
The solutions of this kind of problems often have weak singularity at the initial time. This makes the existing numerical methods with uniform time mesh often lose accuracy. In this paper, we propose and analyze a high-order compact finite difference method with nonuniform time mesh. The time-...