Domain decomposition using a 2-level correction scheme

The PHYSICA software was developed to enable multiphysics modelling allowing for interaction between Computational Fluid Dynamics (CFD) and Computational Solid Mechanics (CSM) and Computational Aeroacoustics (CAA). PHYSICA uses the finite volume method with 3-D unstructured meshes to enable the modelling of complex geometries. Many engineering applications involve significant computational time which needs to be reduced by means of a faster solution method or parallel and high performance algorithms. It is well known that multigrid methods serve as a fast iterative scheme for linear and nonlinear diffusion problems. This papers attempts to address two major issues of this iterative solver, including parallelisation of multigrid methods and their applications to time dependent multiscale problems.

Image denoise by fourth-order PDE based on the changes of laplacian

Fourth-order partial differential equation (PDE) proposed by You and Kaveh (You-Kaveh fourth-order PDE), which replaces the gradient operator in classical second-order nonlinear diffusion methods with a Laplacian operator, is able to avoid blocky effects often caused by second-order nonlinear PDEs. However, the equation brought forward by You and Kaveh tends to leave the processed images with isolated black and white speckles. Although You and Kaveh use median filters to filter these speckles, median filters can blur the processed images to some extent, which weakens the result of You-Kaveh fourth-order PDE. In this paper, the reason why You-Kaveh fourth-order PDE can leave the processed images with isolated black and white speckles is analyzed, and a new fourth-order PDE based on the changes of Laplacian (LC fourth-order PDE) is proposed and tested. The new fourth-order PDE preserves the advantage of You-Kaveh fourth-order PDE and avoids leaving isolated black and white speckles. Moreover, the new fourth-order PDE keeps the boundary from being blurred and preserves the nuance in the processed images, so, the processed images look very natural.