We present a very terse introduction into the basic classes and the mathematical ideas. This is also available on a color poster which prints nicely in A0-A4.
The numerical methods which should be implemented are already formulated in an abstract way based on hierarchical structured mathematical concepts. Therefore, represent each concept by a module and combine the modules according to the numerical algorithm. This defines concept oriented design.
Mathematical Concepts | Fundamental Classes |
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Using a basis | Bilinear form Mesh |
Assembling using T matrices: ![]()
| Assembling the global matrix and the load vector and solving the linear system: The T matrices are built columnwise: each column in a T matrix corresponds to a global degree of freedom: |
The constraints of hanging nodes are eliminated using S matrices: ![]() ![]() ![]() ![]() | S matrices in 1D are computed by solving a linear system. In higher dimensions, tensor product and composition is used: ![]() |
Solving the Maxwell Eigen value problem in a perfect conductor boundary condition domain