Doctor of Philosophy

dissertationThe motivation for this work is the forward and inverse problem for magnetotellurics, a frequency domain electromagnetic remote-sensing geophysical method used in mineral, geothermal, and groundwater exploration. The dissertation consists of four papers. In the first paper, we prove the existence and uniqueness of a representation of any vector field in H(curl) by a vector lying in H(curl) and H(div). It allows us to represent electric or magnetic fields by another vector field, for which nodal finite element approximation may be used in the case of non-constant electromagnetic properties. With this approach, the system matrix does not become ill-posed for lowfrequency In the second paper, we consider hexahedral finite element approximation of an electric field for the magnetotelluric forward problem. The near-null space of the system matrix for low frequencies makes the numerical solution unstable in the air. We show that the proper solution may obtained by applying a correction on the null space of the curl. It is done by solving a Poisson equation using discrete Helmholtz decomposition. We parallelize the forward code on multicore workstation with large RAM. In the next paper, we use the forward code in the inversion. Regularization of the inversion is done by using the second norm of the logarithm of conductivity. The data space Gauss-Newton approach allows for significant savings in memory and computational time. We show the efficiency of the method by considering a number of synthetic inversions and we apply it to real data collected in Cascade Mountains. The last paper considers a cross-frequency interpolation of the forward response as well as the Jacobian. We consider Pade approximation through model order reduction and rational Krylov subspace. The interpolating frequencies are chosen adaptively in order to minimize the maximum error of interpolation. Two error indicator functions are compared. We prove a theorem of almost always lucky failure in the case of the right hand analytically dependent on frequency. The operator's null space is treated by decomposing the solution into the part in the null space and orthogonal to it

Application of HPC in eddy current electromagnetic problem solution

As engineering problems are becoming more and more advanced, the size of an average model solved by partial differential equations is rapidly growing and, in order to keep simulation times within reasonable bounds, both faster computers and more efficient software implementations are needed. In the first part of this thesis, the full potential of simulation software has been exploited through high performance parallel computing techniques. In particular, the simulation of induction heating processes is accomplished within reasonable solution times, by implementing different parallel direct solvers for large sparse linear system, in the solution process of a commercial software. The performance of such library on shared memory systems has been remarkably improved by implementing a multithreaded version of MUMPS (MUltifrontal Massively Parallel Solver) library, which have been tested on benchmark matrices arising from typical induction heating process simulations. A new multithreading approach and a low rank approximation technique have been implemented and developed by MUMPS team in Lyon and Toulouse. In the context of a collaboration between MUMPS team and DII-University of Padova, a preliminary version of such functionalities could be tested on induction heating benchmark problems, and a substantial reduction of the computational cost and memory requirements could be achieved. In the second part of this thesis, some examples of design methodology by virtual prototyping have been described. Complex multiphysics simulations involving electromagnetic, circuital, thermal and mechanical problems have been performed by exploiting parallel solvers, as developed in the first part of this thesis. Finally, multiobjective stochastic optimization algorithms have been applied to multiphysics 3D model simulations in search of a set of improved induction heating device configurations

G-CSC Report 2010

The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems.. The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance

International Workshop on Finite Elements for Microwave Engineering

When Courant prepared the text of his 1942 address to the American Mathematical Society for publication, he added a two-page Appendix to illustrate how the variational methods first described by Lord Rayleigh could be put to wider use in potential theory. Choosing piecewise-linear approximants on a set of triangles which he called elements, he dashed off a couple of two-dimensional examples and the finite element method was born. … Finite element activity in electrical engineering began in earnest about 1968-1969. A paper on waveguide analysis was published in Alta Frequenza in early 1969, giving the details of a finite element formulation of the classical hollow waveguide problem. It was followed by a rapid succession of papers on magnetic fields in saturable materials, dielectric loaded waveguides, and other well-known boundary value problems of electromagnetics. … In the decade of the eighties, finite element methods spread quickly. In several technical areas, they assumed a dominant role in field problems. P.P. Silvester, San Miniato (PI), Italy, 1992 Early in the nineties the International Workshop on Finite Elements for Microwave Engineering started. This volume contains the history of the Workshop and the Proceedings of the 13th edition, Florence (Italy), 2016 . The 14th Workshop will be in Cartagena (Colombia), 2018

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers

Development of an Unsteady Aeroelastic Solver for the Analysis of Modern Turbomachinery Designs

Developers of aircraft gas turbine engines continually strive for greater efficiency and higher thrust-to-weight ratio designs. To meet these goals, advanced designs generally feature thin, low aspect airfoils, which offer increased performance but are highly susceptible to flow-induced vibrations. As a result, High Cycle Fatigue (HCF) has become a universal problem throughout the gas turbine industry and unsteady aeroelastic computational models are needed to predict and prevent these problems in modern turbomachinery designs. This research presents the development of a 3D unsteady aeroelastic solver for turbomachinery applications. To accomplish this, a well established turbomachinery Computational Fluid Dynamics (CFD) code called Corsair is loosely coupled to the commercial Computational Structural Solver (CSD) Ansys® through the use of a Fluid Structure Interaction (FSI) module. Significant modifications are made to Corsair to handle the integration of the FSI module and improve overall performance. To properly account for fluid grid deformations dictated by the FSI module, temporal based coordinate transformation metrics are incorporated into Corsair. Wall functions with user specified surface roughness are also added to reduce fluid grid density requirements near solid surfaces. To increase overall performance and ease of future modifications to the source code, Corsair is rewritten in Fortran 90 with an emphasis on reducing memory usage and improving source code readability and structure. As part of this effort, the shared memory data structure of Corsair is replaced with a distributed model. Domain decomposition of individual grids in the radial direction is also incorporated into Corsair for additional parallelization, along with a utility to automate this process in an optimal manner based on user input. This additional parallelization helps offset the inability to use the fine grain mp-threads parallelization in the original code on non-distributed memory architectures such as the PC Beowulf cluster used for this research. Conversion routines and utilities are created to handle differences in grid formats between Corsair and the FSI module. The resulting aeroelastic solver is tested using two simplified configurations. First, the well understood case of a flexible cylinder in cross flow is studied with the natural frequency of the cylinder set to the shedding frequency of the Von Karman streets. The cylinder is self excited and thus demonstrates the correct exchange of energy between the fluid and structural models. The second test case is based on the fourth standard configuration and demonstrates the ability of the solver to predict the dominant vibrational modes of an aeroelastic turbomachinery blade. For this case, a single blade from the fourth standard configuration is subjected to a step function from zero loading to the converged flow solution loading in order to excite the structural modes of the blade. These modes are then compared to those obtained from an in vacuo Ansys® analysis with good agreement between the two

HPCCP/CAS Workshop Proceedings 1998

This publication is a collection of extended abstracts of presentations given at the HPCCP/CAS (High Performance Computing and Communications Program/Computational Aerosciences Project) Workshop held on August 24-26, 1998, at NASA Ames Research Center, Moffett Field, California. The objective of the Workshop was to bring together the aerospace high performance computing community, consisting of airframe and propulsion companies, independent software vendors, university researchers, and government scientists and engineers. The Workshop was sponsored by the HPCCP Office at NASA Ames Research Center. The Workshop consisted of over 40 presentations, including an overview of NASA's High Performance Computing and Communications Program and the Computational Aerosciences Project; ten sessions of papers representative of the high performance computing research conducted within the Program by the aerospace industry, academia, NASA, and other government laboratories; two panel sessions; and a special presentation by Mr. James Bailey

Numerical Simulations of Hypersonic Aerothermoelastic Phenomena

This dissertation examines the following subjects important to hypersonic aerothermoelastic flows: aerodynamic heating on a double-wedge airfoil, active cooling on a double-wedge airfoil, and aerothermoelastic panel utter with deformable supports. To facilitate this examination, an aerothermoelastic solver was created by coupling solvers for the structural elasticity and thermal diffusion equations to a Reynolds averaged Navier-Stokes (RANS) solver. Validation studies were performed on the aerodynamic, aerothermal, and aerothermoelastic configurations of the solver, which were then used to investigate the aforementioned subjects. The aerodynamic solver was validated for hypersonic heating simulations by comparison to the Fay-Riddell equation for the peak heat flux on a circular cylinder and by comparison to compressible boundary layer ow for heat flux into a at plate. A novel investigation was then performed of the heat flux on a double-wedge airfoil, looking at variations of heat flux due to angle of attack, wall temperature, Mach number, and altitude. The aerothermal solver was validated using experimental and computational data from the hypersonic heating of a spherical protuberance on a flat plate. The solver was then used in a novel study to analyze the effect of active cooling on the steady-state skin temperature of a double-wedge airfoil in hypersonic flow. Active cooling using a piecewise continuous cooling distribution resulted in sufficient temperature reduction, but also results in significant chordwise temperature gradients. The aerothermoelastic solver was validated using computational data from the analysis of panel utter. The solver was then used to examine the effects of deformable structural supports on the utter dynamics of the panel for the first time. Deformable supports along existing simply-supported boundaries were shown to be ineffective at improving resistance to utter or buckling. Deformable supports within a panel were shown to increase the utter resistance threefold and buckling resistance almost fivefold