Master Thesis Calderon Preconditioning for Higher Order Boundary Element Method
نویسنده
چکیده
2 Hierarchical Preconditioner for Scalar Bases 3 2.1 General Hierarchical Preconditioner Formula . . . . . . . . . . . 3 2.2 Hierarchical Splitting in Case of Nodal Basis Functions . . . . . 4 2.3 Hierarchical Preconditioner Formula for Bases of Nodal Basis Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.1 Projection Matrix Pc . . . . . . . . . . . . . . . . . . . . 7 2.4.2 Matrix T Local . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.3 Inverse Block Diagonal Submatrix . . . . . . . . . . . . . 8 2.4.4 Assembling matrices . . . . . . . . . . . . . . . . . . . . . 9 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5.1 Validation Model . . . . . . . . . . . . . . . . . . . . . . 9 2.5.2 Test Models: Constant Basis . . . . . . . . . . . . . . . . 10 2.5.3 Test Models: Linear Basis . . . . . . . . . . . . . . . . . 13 2.5.4 Test Models: Quadratic Basis . . . . . . . . . . . . . . . 16 2.5.5 Industrial Application . . . . . . . . . . . . . . . . . . . . 19
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