Solving parabolic problems with different time steps in different regions in space based on domain decomposition methods
Copyright policy )Solving parabolic problems with different time steps in different regions in space based on domain decomposition methods
The paper deals with the numerical solution of systems of nonlinear parabolic equations having the form \[ u_t+ f(t, x, y,u,u_x, u_y)= [D_1(t, x,y,u) u_x]_x+ [D_2(t, x,y,u) u_y]_y, \] equipped with some initial conditions and boundary conditions of mixed type. It is supposed that the matrices \(D_1\), \(D_2\) are positive definite. After describing the proposed algorithms, the author presents a number of numerical examples.
- Rensselaer Polytechnic Institute United States
mixed initial-boundary value problems, numerical examples, systems of nonlinear parabolic equations, extrapolation methods, overlapping domain decomposition, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, Nonlinear parabolic equations, finite element methods, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, multiplicative Schwarz algorithm, local adaptivity, parallel computation
mixed initial-boundary value problems, numerical examples, systems of nonlinear parabolic equations, extrapolation methods, overlapping domain decomposition, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, Nonlinear parabolic equations, finite element methods, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, multiplicative Schwarz algorithm, local adaptivity, parallel computation
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