3.3.1 Reference Mapping Strategy



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3.3.1 Reference Mapping Strategy

  The generation of the grid used for the solution of the physical equations is separated into two tasks [Wim91b]. The first task is the generation of a mapping from physical domain to computational domain and vice versa. This mapping is described by the functions and . To generate the mapping we use an approximately equidistant grid in the computational domain which is just fine enough to resolve all geometric details (uv-geo in Figure 3.3-4). This grid is mapped onto the physical domain (xy-geo in Figure 3.3-4) using algebraic, elliptic or variational methods such that the points at the boundaries are approximately equidistributed along the arc length (cf. Section 3.3.3). This geometry grid establishes the mapping function , , i.e. it serves as reference mapping.

The second task is the generation and adaption of the grid for solving the physical equations (physics grid). A gradient resolution criterion and a dose conservation criterion control the adaption of the grid according to the evolving dopant profiles. After each time step during a transient simulation the adaption is achieved by inserting and deleting lines in the computational domain (uv-phys in Figure 3.3-4). The corresponding grid points in the physical domain (xy-phys in Figure 3.3-4) are obtained by interpolation in the geometry grid.

 

Actually, we could generate the mapping using the physical grid, too. The reason why we are using an independent geometry grid is twofold: (1) In many applications the geometry (physical domain) is stationary, i.e. the geometry does not change with time. Then, the mapping has to be calculated just once for the whole simulation. (2) For non-algebraic mapping methods the point position for a given may depend on the grid. This dependency entails that the position for a point can change each time a grid update for the physical quantities is made. The application of a separate grid for establishing the mapping function guarantees an unambiguous mapping from computational domain to physical domain.



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Next: 3.3.2 Differential Geometric Notation Up: 3.3 Transformation Method Previous: 3.3 Transformation Method



Martin Stiftinger
Wed Oct 19 13:03:34 MET 1994