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- Boundaries
- @digest: c1ecd3f776511f977c2a64dcd40426f2
- @id: 147693
- @mdate: 2001-07-22T09:26:24Z
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- description: Boundaries
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- keywords: tutorial
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- #keywords: permeability (22172), solenoid (20578), pdnmesh (15402), electro (10493), yatawatta (5713), permittivity (5069), boundaries (5001), boundary (4642), refined (4582), density (3709), electrostatic (3476), magnetic (2142), outer (1970), figure (1698), edges (1526), observe (1472), iron (1450), differential (954), closed (837), problem (807), equation (601), splitting (536), given (481), solution (433), inverse (421), material (397), introduce (355), installation (281), current (276), determined (266), specified (244), represent (232)
- Next: Installation Up: A Simple Example Previous: Edges Boundaries Finally, in the input file, we should specify the boundary detail. Boundaries need not be closed except the outer one, but almost always they are closed. Boundaries are required to define the shape of the problem as well as the material properties of the problem. For instance, in this problem, There are two boundaries as given in figure 1 . The point set 0, 1, 2, and 3 specify the outer boundary and the point set 4, 5, 6 and 7 represent the solenoid core. Always, the outer boundary will be need to be specified and this should be done before other boundaries. For any material, two parameters must be specified. For instance, in an electro-magnetic problem, they can be the permeability and the current density and for an electrostatic problem, they can be the permittivity and the charge density. In fact, for an electro-magnetic problem, the inverse of the permeability should be given. For any other problem, the values need to be given can be determined depending on the differential equation. Figure 5: The boundary data The boundary data for this problem is given in figure 5 . First the number of boundaries is specified. Next the outer boundary detail is given. The outer boundary has four edges, it is closed, its 1/permeability is 1.0 and its current density is 0. Next, the numbers of the edges in that boundary is given line by line. The general format for boundary information is (number of edges) (closed) (1/permeability) (current density) Hence, we can see that the inner boundary has 0.1 as its 1/permeability value and 0 as its current density. The complete data file is given in figure 6 Figure 6: The data file Now, we can run pdnMesh and give this file as its input and see if we get the answer. First run it by typing ./pdnmesh -i your_file and observe the output. If you need a more refined mesh try giving a high splitting priority as follows. ./pdnmesh -s 0.6 -i your_file Now you will see a more refined solution. As an extension, we could introduce an iron block close to the solenoid to observe the change in the field pattern. The new data file is given in figure 7 . Now we have three boundaries and 12 points. Figure 7: The new data file The solution will look like the one given in figure 8 Figure 8: The solenoid field with an iron block Next: Installation Up: A Simple Example Previous: Edges Sarod Yatawatta 2001-06-10
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http://www.gnu.org/savannah-checkouts/non-gnu/pdnmesh/non-gnu/pdnmesh/tutorial/node5.html
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