Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Scalable Parallel Domain Decomposition Methods for Numerical Simulation of PDEs

This paper is concerned about scalable parallel domain decomposition methods for numerical simulation of PDEs. First, one level and two level scalable parallel domain decomposition methods which can be used to solve different equations, are introduced in detail, and then we explain Krylov subspace accelerator technique used to improve the convergence of the methods. Last, the results of some nu...

Meshless Methods Coupled with Other Numerical Methods

Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree m...

The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method for the Numerical Solution of PDEs

We present a generalization of the RBF-FD method that allows full control of the overlap between RBF-FD stencils. We accomplish this by introducing a continuous overlap parameter δ ∈ [0, 1] such that δ = 1 recovers the standard RBF-FD method and δ = 0 results in a full decoupling of the RBF-FD stencils. We show with a simple example that global interpolation with both RBFs and RBFs augmented wi...

Numerical Methods for PDEs