An Hp-Adaptive Finite Element Procedure For Fluid-Structure Interaction In Fully Eulerian Framework

This thesis attempts to implement a fully automatic hp-adaptive finite element procedure for fluid-structure interaction (FSI) problems in two dimensions. This work hypotesizes the efficacy of Fully Eulerian framework of FSI in hp-adaptivity on an a posteriori error estimator and adaptation for minimization of error in energy norm. Automatic mesh adaptation over triangular elements is handled by red-green-blue (RGB) refinement method. An effective mesh adaptivity to avoid excessive growth of unknowns is also addressed. Since the hp-method uses high order polynomials as approximation functions, the resulting system matrices are less sparse leading to the notion of FSI computation with parallelism. The parallel hp-adaptive computation is assessed with the conventional uniform and h refinement on a number of benchmark test cases. Subsequently, the efficacy of the fully Eulerian framework is compared to the well known Arbitrary Lagrangian Framework( ALE) for two different material models, namely, the St. Venant Kirchoff and the Neo-Hookean models. It was found that the fully Eulerian framework provides accurate FSI predictions for large deformation without need of frequent remeshing. The hp-adaptive method was also found to be a viable approach in obtaining accurate solutions without much compromise in computer memory and time. Furthermore, the integration of parallelism is successful in reducing the computation time by up to two orders of magnitude relative to the serial solver. For the comparisons between the ALE and the fully Eulerian frameworks, the computed solutions in all test cases are observed to be in agreement with each other

Energy-norm-based and goal-oriented automatic hp adaptivity for electromagnetics: Application to waveguide Discontinuities

The finite-element method (FEM) enables the use of adapted meshes. The simultaneous combination of h (local variations in element size) and p (local variations in the polynomial order of approximation) refinements, i.e., hp-adaptivity, is the most powerful and flexible type of adaptivity. In this paper, two versions of a fully automatic hp-adaptive FEM for electromagnetics are presented. The first version is based on minimizing the energy-norm of the error. The second, namely the goal oriented strategy, is based on minimizing the error of a given (user-prescribed) quantity of interest. The adaptive strategy delivers exponential convergence rates for the error, even in the presence of singularities. The hp adaptivity is presented in the context of 2-D analysis of H -plane rectangular waveguide discontinuities. Stabilized variational formulations and H(curl) FEM discretizations in terms of quadrilaterals of variable order of approximation supporting anisotropy and hanging nodes are used. Comparison of energy-norm and goal-oriented hp-adaptive strategies in the context of waveguiding problems is provided. Specifically, the scattering parameters of the discontinuity are used as goal

Goal-oriented self-adaptive hp-strategies for finite element analysis of electromagnetic scattering and radiation problems

In this paper, a fully automatic goal-oriented hp-adaptive finite element strategy for open region electromagnetic problems (radiation and scattering) is presented. The methodology leads to exponential rates of convergence in terms of an upper bound of an user-prescribed quantity of interest. Thus, the adaptivity may be guided to provide an optimal error, not globally for the field in the whole finite element domain, but for specific parameters of engineering interest. For instance, the error on the numerical computation of the S-parameters of an antenna array, the field radiated by an antenna, or the Radar Cross Section on given directions, can be minimized. The efficiency of the approach is illustrated with several numerical simulations with two dimensional problem domains. Results include the comparison with the previously developed energy-norm based hp-adaptivity

Goal-oriented self-adaptive hp finite element simulation of 3D DC borehole resistivity simulations

In this paper we present a goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and a parallel multi-frontal direct solver. The algorithm automatically generates (without any user interaction) a sequence of meshes delivering exponential convergence of a prescribed quantity of interest with respect to the number of degrees of freedom. The sequence of meshes is generated from a given initial mesh, by performing h (breaking elements into smaller elements), p (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal-oriented adaptivity and the solver work fully in parallel. We describe the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. We apply the methodology described to the three-dimensional simulation of the borehole resistivity measurement of direct current through casing in the presence of invasion. © 2011 Published by Elsevier Ltd

Goal-oriented hp-adaptivity for elliptic problems

Abstract We propose and test a fully automatic, goal-oriented hp-adaptive strategy for elliptic problems. The method combines two techniques: the standard goal-oriented adaptivity based on a simultaneous solution of a dual problem, and a recently proposed hp-strategy based on minimizing the projection-based interpolation error of a reference solution. The proposed strategy is illustrated with two numerical examples: Laplace equation in L-shape domain, and an axisymmetric Maxwell problem involving radiation of a loop antenna wrapped around a metallic cylinder into a conductive medium

Computation of forces in strongly nonlinear magnetic fields using higher-order eggshell algorithm

A novel version of the eggshell-based procedure for numerical computation of magnetic forces and torques acting on ferromagnetic bodies in highly nonlinear magnetic fields is presented. The procedure works with a fully adaptive higher-order finite element method developed for years in our research group, that is implemented in own code Agros2D and library Hermes. The power of the methodology and both codes is demonstrated on the solution of two typical examples: computation of the static characteristic of a magnetic actuator and torque characteristic of a flux-switched permanent-magnet machine. The results obtained are compared with data calculated by several other available codes

An hphp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems

In this paper we develop an $hp$-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an $hp$-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully $hp$-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.Comment: arXiv admin note: text overlap with arXiv:1408.522