S. Wagner, T. Grasser, C. Fischer, and S. Selberherr (Austria)
Partial Differential Equations, Finite Boxes Discretization, Boundary Conditions, Linear Equation Systems
We present a generally applicable approach which allows to efficiently assemble equations necessary for solving a sys tem of nonlinear partial differential equations discretized on a grid. Since the nonlinear problem is usually solved by a damped Newton algorithm the solution of a linear equa tion system has to be obtained at each step. Our assem bly approach for these systems has been originally devel oped for the simulation of semiconductor devices based on the Finite Boxes discretization scheme. It has been rig orously implemented in a simulator module which is cur rently used in the general purpose device and circuit simu lator MINIMOS-NT. In addition to the assembly itself, sev eral requirements of the simulation process, namely the representation of boundary conditions, physically moti vated variable transformation, and numerical conditioning, are taken into account.
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