Application of higher order hierarchical vector finite element method in multicomponent electromagnetic induction problem

Multicomponent induction logging responses are simulated by using higher order hierarchical vector finite element method (FEM). To improve computational efficiency, hierarchical mixed order vector basis functions are applied to FEM. Different order basis functions are used in different elements in accordance with the changing speed of the field. The mixed order scheme reduces greatly the number of unknowns without reducing accuracy, and can attain much higher computational efficiency. The numerical results shown demonstrate the validity and efficiency of the scheme.