Die Anwendung von Krylov Unterraum Methoden zur Berechnung von Forwärts Lösungen und Model Sensitivitäten von 3D mariner, aktiver elektromagnetischer Probleme im Zeitbereich

To reduce the run-times of 3D modeling and inversion software for the interpretation of marine controlled source electromagnetics (CSEM) in time domain, the implementation of efficient algorithms on massive parallel hardware is presented. Two forward modeling implementations as well as an implementation for sensitivity calculation are illustrated. The first forward code is an implementation of the spectral Lanczos decomposition method on a graphics processing unit (GPU). The applicability of the code for a CSEM system, how it is used at GEOMAR, is demonstrated. In the second forward code, the SLDM is replaced by the more efficient Rational Krylov Subspace Method (RKSM). This reduces the dimension and run-time of the problem drastically. The accuracy of the code is investigated for different models and conductivity contrasts. The run-times of SLDM and RKSM are compared on different architectures. The sensitivities are computed with the MOR-method (Model Order Reduction). It is shown that the method works and the applicability to a real data set is shown.Zur Reduzierung der Laufzeiten von 3D Modellierungs- und Inversions-Software für die Interpretation von mariner, aktiver Elektromagnetik (engl. CSEM, controlled source electro magnetics) im Zeitbereich, werden effiziente Algorithmen und Implementierungen auf massiv-paralleler Hardware vorgestellt. Zwei Implementierungen zur Berechnung der Vorwärts Modellierung, sowie eine Implementierung zur Berechnung der Sensitivitäten werden dargestellt. Bei dem ersten Vorwärts Code handelt es sich um eine Implementierung der Spektralen Lanczos Zerlegung (engl. SLDM, Spectral Lanczos Decomposition Method) auf dem Prozessor von Graphik Karten (engl. GPU, Graphics Processing Unit). Die Anwendbarkeit des Codes wird für ein CSEM System demonstriert, wie es am GEOMAR im Einsatz ist. Bei dem Zweiten Vorwärts Code wird die SLDM durch das effektivere Rationale Krylov Unterraum Verfahren (engl. RKSM, Rational Krylov Subspace Method) ersetzt. Die Genauigkeit des Codes wird für verschiedene Modelle und Kontraste des elektrischen Leitwertes untersucht. Ein Laufzeitvergleich von SLDM und RKSM wird gegeben.Die Sensitivitäten werden mit dem MOR-Verfahren (engl. Model Order Reduction) berechnet. Es wird gezeigt, dass die Methode funktioniert und seine Anwendbarkeit auf einen echten Datensatz demonstriert

The application of Krylov subspace methods for the calculation of forward solutions and model sensitivities of 3D time domain marine controlled source electromagnetic problems

To reduce the run-times of 3D modeling and inversion software for the interpretation of marine controlled source electromagnetics (CSEM) in time domain, the implementation of efficient algorithms on massive parallel hardware is presented. Two forward modeling implementations as well as an implementation for sensitivity calculation are illustrated. The first forward code is an implementation of the spectral Lanczos decomposition method on a graphics processing unit (GPU). The applicability of the code for a CSEM system, how it is used at GEOMAR, is demonstrated. In the second forward code, the SLDM is replaced by the more efficient Rational Krylov Subspace Method (RKSM). This reduces the dimension and run-time of the problem drastically. The accuracy of the code is investigated for different models and conductivity contrasts. The run-times of SLDM and RKSM are compared on different architectures. The sensitivities are computed with the MOR-method (Model Order Reduction). It is shown that the method works and the applicability to a real data set is shown

Investigating Schwarz domain decomposition based preconditioners for efficient geophysical electromagnetic field simulation

In this thesis, I researched and implemented a number of Schwarz domain decomposition algorithms with the intent of finding an efficient method to solve the geophysical EM problem. I began by using finite difference and finite element discretizations to investigate the domain decomposition algorithms for the Poisson problem. I found that the Schwarz methods were best used as a preconditioner to a Krylov iteration. The optimized Schwarz (OS) preconditioner outperformed the related restricted additive Schwarz (RAS) preconditioner and both of the local and global OS fixed point iterations. Using finite differences the OS preconditioner performed much better than the RAS preconditioner, but using finite element in parallel with the FEniCS assembly library, their performance was similar. The FEniCS library automatically partitions the global mesh into subdomains and produces irregular partition boundaries. By creating a serial rectangular subdomain code in FEniCS, I regained the benefit of the OS preconditioner, suggesting that the irregular partitioning scheme was detrimental to the convergence behaviour of the OS preconditioner. Based on my work for the Poisson problem, I decided to attempt both a RAS and OS preconditioned GMRES iteration for the electromagnetic problem. Due to the unstructured meshes and source/receiver refinement used in EM modelling I could not avoid the irregular mesh partitioning, and the OS preconditioner lagged the RAS preconditioner in terms of iteration count. On the bright side, the RAS preconditioner worked very well, and outperformed any of the preconditioners bundled with PETSc in terms of both iteration count and time to solution

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest

[Research activities in applied mathematics, fluid mechanics, and computer science]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995

[Activity of Institute for Computer Applications in Science and Engineering]

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science

Wave Propagation in Materials for Modern Applications

In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas