A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM

We present an application of fully anisotropic hp-adaptivity over quadrilateral meshes for H(curl)-conforming discretizations in Computational Electromagnetics (CEM). Traditionally, anisotropic h-adaptivity has been difficult to implement under the constraints of the Continuous Galerkin Formulation; however, Refinement-by-Superposition (RBS) facilitates anisotropic mesh adaptivity with great ease. We present a general discussion of the theoretical considerations involved with implementing fully anisotropic hp-refinement, as well as an in-depth discussion of the practical considerations for 2-D FEM. Moreover, to demonstrate the benefits of both anisotropic h- and p-refinement, we study the 2-D Maxwell eigenvalue problem as a test case. The numerical results indicate that fully anisotropic refinement can provide significant gains in efficiency, even in the presence of singular behavior, substantially reducing the number of degrees of freedom required for the same accuracy with isotropic hp-refinement. This serves to bolster the relevance of RBS and full hp-adaptivity to a wide array of academic and industrial applications in CEM<br>

A Refinement-by-Superposition Approach to Fully Anisotropic hp-Refinement for Improved Efficiency in CEM

We present an application of fully anisotropic hp-adaptivity over quadrilateral meshes for H(curl)-conforming discretizations in Computational Electromagnetics (CEM). Traditionally, anisotropic h-adaptivity has been difficult to implement under the constraints of the Continuous Galerkin Formulation; however, Refinement-by-Superposition (RBS) facilitates anisotropic mesh adaptivity with great ease. We present a general discussion of the theoretical considerations involved with implementing fully anisotropic hp-refinement, as well as an in-depth discussion of the practical considerations for 2-D FEM. Moreover, to demonstrate the benefits of both anisotropic h- and p-refinement, we study the 2-D Maxwell eigenvalue problem as a test case. The numerical results indicate that fully anisotropic refinement can provide significant gains in efficiency, even in the presence of singular behavior, substantially reducing the number of degrees of freedom required for the same accuracy with isotropic hp-refinement. This serves to bolster the relevance of RBS and full hp-adaptivity to a wide array of academic and industrial applications in CEM<br>

Extended Meshfree Approach for Crack Statistical Analysis of Anisotropic Functionally Graded Brazilian Disc Subjected to Traction Load

An extended meshless method that relying upon Galerkin formulation is applied on the crack analysis of orthotropic functionally graded Brazilian disc. Weak form is involved to solve the governing equation in the numerical method. In addition, enrichment terms and sub-triangle techniques are applied to improve the accuracy of relevant results. This paper depicts the influence of variation in the crack stretch and non-homogeneity parameters on the values of stress intensity factors using a developed MATLAB program. In the isotropic case, it is clear that when the length of crack increases, SIF increases. Graduation in has more effect in increasing the values of SIF in corresponding increased crack length. The verification has been checked by changing the range of the J-integral domain and variation of the support domain.

Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem

In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes.