Research And Application Of Adaptive Mesh Technology In Computational Electromagnetics

As the model of the object gets more and more complex and requires higher computational accuracy,not only is it necessary to explore more efficient and accurate numerical computation methods,but also to obtain higher quality mesh in the field of numerical computation including computational electromagnetics.On the one hand,it is quite complicated to obtain high-quality meshes by traditional profiling using Hypermesh mesh software,and on the other hand,Hypermesh mesh software only profiles according to geometry without considering physical properties,which makes it difficult to achieve the required accuracy for the electromagnetic simulation problems of multi-scale complex objects such as ships,unmanned aerial vehicles,large-scale integrated chips and antenna arrays.Exploring efficient and accurate adaptive meshing techniques can help improve the computational accuracy to meet the needs of complex computation and engineering applications.In this thesis,some relevant research has been done around adaptive mesh techniques for integral equations in the field of computational electromagnetics,as follows.Domain decomposition method of the Discontinuous Galerkin Integral Equation is first researched to build the foundation of the computational method for the optimization of the later refined non-conformal mesh.Starting from the Discontinuous Galerkin Integral Equation,the half-RWG basis functions applied,the pairwise pairing principle,and the establishment of internal penalty terms are introduced,and the matrix equations and discrete expressions are obtained for non-conformal adaptive refined mesh of complex multi-scale targets.Then the equations and discrete expressions of the domain decomposition method of the Discontinuous Galerkin Integral Equation are derived,and the preprocessing method of the matrix equation is introduced.Several object models with different shape complexity are computed using the method,and the method is verified to have good accuracy by non-conformal partitioning.It enables the computation of non-conformal mesh objects.Then the adaptive mesh technique is researched,which is divided into two parts: the design of the error estimator and the refinement method of the mesh.In the first part,three error estimators based on discontinuous current estimation,discontinuous charge-based error estimation,and field-based residual error estimation are discussed,and the three methods are verified as adaptive refinement criteria through relevant experimental tests.In the second part,the refinement method of the mesh based on error estimation is discussed.The problem mesh identified by the error estimator is refined by taking the midpoint of three sides of the triangular mesh cell and dividing it into four,and iterating through the loop until the desired accuracy is achieved.At last,the proposed method is verified by relevant numerical examples,which has good accuracy.It reduces the number of unknowns and saves memory resources.Finally,the research work of the thesis is summarized and further investigation of adaptive mesh technology is prospected.