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Fig. 1. Division of the solution domain and the shape functions. To retain the required mathematical properties o f the entire bases in terms of the consistency and the linear independence, the bridging scale concept as proposed in [6] is used the wavelets. The basic concept of the bridging scal Q ent on some projection operator P to represent the to modify es is based on a hierarchical decomposition of a function u which is depen- projection the solution variable into two different parts, i.e., the approximated by wavelets and the one that is represe shape functions, one employs the property of a proje of u onto the span of some set of basis functions. To decompose one that is nted by FE ction oper- ator such that multiple projections of the function will leave the function unchanged [6], i.e., PPu = Pu. By using this con- cept, the total function u of (3) can now be reformulated as

Figure 1 Division of the solution domain and the shape functions. To retain the required mathematical properties o f the entire bases in terms of the consistency and the linear independence, the bridging scale concept as proposed in [6] is used the wavelets. The basic concept of the bridging scal Q ent on some projection operator P to represent the to modify es is based on a hierarchical decomposition of a function u which is depen- projection the solution variable into two different parts, i.e., the approximated by wavelets and the one that is represe shape functions, one employs the property of a proje of u onto the span of some set of basis functions. To decompose one that is nted by FE ction oper- ator such that multiple projections of the function will leave the function unchanged [6], i.e., PPu = Pu. By using this con- cept, the total function u of (3) can now be reformulated as

Related Figures (4)

Fig. 3. Partition of the solution domain and the corresponding mesh used by the proposed combined wavelet-EFG method. Fig. 2. Schematic diagram of the end region of a power transformer being studied.
Fig. 3. Partition of the solution domain and the corresponding mesh used by the proposed combined wavelet-EFG method. Fig. 2. Schematic diagram of the end region of a power transformer being studied.
Fig. 5. Comparison of computed results between the proposed algorithm and standard FEM for the power transformer prototype problem. Fig. 4. Mesh used by the standard FEM for comparison purposes.
Fig. 5. Comparison of computed results between the proposed algorithm and standard FEM for the power transformer prototype problem. Fig. 4. Mesh used by the standard FEM for comparison purposes.
Related topics:
EngineeringComputer ScienceMeshless methodThe Element free Galerkin MethodLinear IndependenceNumerical Calculationmoving least squares approximation (MLS)
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