In this paper, several local and parallel finite element algorithms are proposed and analyzed for the 2D/3D stationary inductionless incompressible magnetohydrodynamic (MHD) equations. The core concept is to guarantee the charge-conservation property by choosing mixed finite element spaces in H 0 (div , Ω) × L 0 2 (Ω) to approximate (J , ϕ) , meantime combining the idea of domain decomposition method to realize parallel operation. The characteristic of the proposed algorithms is that the computational complexity is greatly reduced while ensuring the accuracy of the numerical simulation. With the local a prior estimate as the technical means of theoretical analysis, we give the error estimates of the algorithms. Finally, several numerical experiments are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]
Abstract In this paper, we have designed a simple method for the inverse scattering problem of stratified ocean waveguide. The simple approach applies the bisection technique in parallel to estimate the boundaries of inhomogeneous media from the received partial data. In addition, the algorithm only involves the matrix–vector operations and possesses the optimal computation complexity in both two and three dimensions. In practice, it is easy to carry out, robust against noise and capable of reconstructing the penetrable obstacles of different locations and shapes. We can consider the simple method as a direct and straightforward process to supply satisfactory initial positions for the implementation of any existing more refined but computationally more demanding techniques to achieve accurate reconstructions of physical features of scatterers. [ABSTRACT FROM AUTHOR]
In this paper, we present two novel symbolic computational algorithms to solve periodic pentadiagonal (PP) linear systems. These two algorithms are based on a special matrix decomposition and the use of any fast pentadiagonal linear solver, respectively. Some numerical examples are given in order to demonstrate the performance of the proposed algorithms and their competitiveness with existing algorithms. All of the experiments are performed on a computer workstation with the aid of programs written in MATLAB. [ABSTRACT FROM AUTHOR]