Automatic grid control for finite differences meshes is a difficult task because only very few mathematically founded criteria for adaptive grid refinement can be given which may be implemented in a computer program with reasonable effort. Especially for the solution of the semiconductor equations, a coupled system of nonlinear partial differential equations, most strategies for fully automatic...

We consider energy-conserving semi-discretizations of linear wave equations on nonuniform grids. Specifically we study explicit and implicit skew-adjoint finite difference methods, based on the assumption of an underlying smooth mapping from a uniform grid, applied to the first and second order wave equations. Our interest is in internal reflection of energy at abrupt variations in grid spacing...

We design a wavelet optimized finite difference (WOFD) scheme for solving self-adjoint singularly perturbed boundary value problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Small dissipation of the solution is captured significantly using an adaptive grid. The adaptive feature is performed automatically by thresholding the wavele...

In this paper, we provide a maximum norm analysis of a finite difference scheme defined on overlapping nonmatching grids for second order elliptic equations. We consider a domain which is the union of p overlapping subdomains where each subdomain has its own independently generated grid. The grid points on the subdomain boundaries need not match the grid points from adjacent subdomains. To obta...

This paper presents a simple model predictive control (MPC) approach to control the power injection system (PIS) for renewable energy applications. A DC voltage source and a single-phase inverter that is connected to the grid by an LCL filter form the PIS. Grid voltage is considered a disturbance for the system. For eliminating this disturbance, a modified model is proposed. It is usual to ...

This paper presents a simple model predictive control (MPC) approach to control the power injection system (PIS) for renewable energy applications. A DC voltage source and a single-phase inverter that is connected to the grid by an LCL filter form the PIS. Grid voltage is considered a disturbance for the system. For eliminating this disturbance, a modified model is proposed. It is usual to ...

In this paper, two-dimensional turbulent flows in different and complex geometries are simulated by using an accurate grid generation method. In order to analyze the fluid flow, numerical solution of the continuity and Navier-Stokes equations are solved using CFD techniques. Considering the complexity of the physical geometry, conformal mapping is used to generate an orthogonal grid by means of...

In this paper, we consider the firefighter problem on a graph G = (V,E) that is either finite or infinite. Suppose that a fire breaks out at a given vertex v ∈ V . In each subsequent time unit, a firefighter protects one vertex which is not yet on fire, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefighter is to save as many vertices as...