Application Research Of The Coupling Of Discontinuous Galerkin Method And Boundary Element Method

This thesis is devoted to enrich the numerical methods used in unbounded domains PDE problems with complex media and avoid the inaccuracy caused by the adopted of artificial boundary condition.We developed a coupling of hybirdizable discontinuous Galerkin(HDG)method and boundary element method,designed and analyzed the numerical investigation of time-harmonic electromagnetic wave propagation problems,especially the electromagnetic scattering problems.HDG methods has many advantages,such as adaptivity to complex geometries through the use of unstructured possibly non-conforming meshes,easily obtained high order accuracy,hp-adaptivity and natural parallelism.HDG methods introduce an additional hybrid variable on the faces of the elements,on which the definition of the local solutions is based and HDG methods produce a linear system in terms of the DOFs of the additional hybrid variable only.The main feature of our present work is to show that the HDG method and the BEM can be coupled naturally with the hybridization through the border of elements.The main idea is to solve the linear system in terms of the DOFs of the additional hybrid variable only,then we can use them to calculate the value of electromagnetic field.It is greatly reduced the number of globally coupled DOFs as well as save both CPU time and memory cost compared to a DG method.We gave the formulation and implementation of HDG-EFIE and studied the well posedness of the HDG-CFIE formulation.The numerical simulations demonstrated that the coupling method works well with the electromagnetic scattering problems in unbounded domains and complex media.The accuracy of the HDG-BEM method had also been proved in the numerical investigation.