Martin Weiser – författare

Thistextbook expands the standard work on numerical mathematics to include the numerics of partial differential equations. The volume is intended for students of mathematics as well as physicists, chemists and engineers who are confronted with finding efficient solutions for complex application problems.

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence.Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted.The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence.

Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted.

The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave. Contents:Finite Element FundamentalsGrids and Finite ElementsAssemblySolversError EstimationMesh RefinementMultigridElastomechanicsFluid MechanicsGrid Data StructureFunction Reference

All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave.

Contents:Finite Element FundamentalsGrids and Finite ElementsAssemblySolversError EstimationMesh RefinementMultigridElastomechanicsFluid MechanicsGrid Data StructureFunction Reference

All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave.

Contents:Finite Element FundamentalsGrids and Finite ElementsAssemblySolversError EstimationMesh RefinementMultigridElastomechanicsFluid MechanicsGrid Data StructureFunction Reference

Das Lehrbuch behandelt adaptive Algorithmen für die numerische Lösung von elliptischen und parabolischen Gleichungen, wobei der Schwerpunkt auf der algorithmischen Effizienz liegt und die notwendige Theorie so elementar wie möglich gehalten wird. Die zweite Ausgabe wurde korrigiert und um eine constraints-basierte Formulierung der Dirichlet-Randbedingungen und einen Abschnitt über spektrale verzögerte Korrekturmethoden erweitert.

Das Lehrbuch behandelt adaptive Algorithmen für die numerische Lösung von elliptischen und parabolischen Gleichungen, wobei der Schwerpunkt auf der algorithmischen Effizienz liegt und die notwendige Theorie so elementar wie möglich gehalten wird. Die zweite Ausgabe wurde korrigiert und um eine constraints-basierte Formulierung der Dirichlet-Randbedingungen und einen Abschnitt über spektrale verzögerte Korrekturmethoden erweitert.

Das Lehrbuch behandelt adaptive Algorithmen für die numerische Lösung von elliptischen und parabolischen Gleichungen, wobei der Schwerpunkt auf der algorithmischen Effizienz liegt und die notwendige Theorie so elementar wie möglich gehalten wird. Die zweite Ausgabe wurde korrigiert und um eine constraints-basierte Formulierung der Dirichlet-Randbedingungen und einen Abschnitt über spektrale verzögerte Korrekturmethoden erweitert.

Mathematical optimization and machine learning are closely related. This proceedings volume of the Thematic Einstein Semester 2023 of the Berlin Mathematics Research Center MATH+ collects recent progress on their interplay in topics such as discrete optimization, nonlinear programming, optimal control, first-order methods, multilevel optimization, machine learning in optimization, physics-informed learning, and fairness in machine learning.

Essay from the year 2007 in the subject History of Germany - National Socialism, World War II, grade: 1, University of Nottingham, language: English, abstract: The 20th century is sometimes called the "e;centrury of genocide"e;. Never before have people been killing each other on such a scale, with so sophisticated methods and techniques, for so many reasons and seemingly without any scrupules or mercy. Untold masses of humans fell victims to these massacres. From South West Africa and Armenia to Cambodia and Rwanda, there were a number of genocides. A number of genocides, but just one Holocaust. Or, was there just one?Most of the scholarly attention devoted to the subject of Holocaust has, not surprisingly, been focused on the Jewish experience during the Nazi period. The study of the Gypsy experience during the same period has been largely underrepresented in the historiography discussions. Therefore, in this paper I will concentrate on the Porrajmos. The main aim of this work is to find out if and eventually to what extent the Shoah and the Porrajmos are comparable. In the first half I deal with the persecution of the Gypsies solely. I describe the main characteristics of the treatment of the Gypsies by the Nazis as well as mention the main laws and decrees that dealt with the issue. In the second part of this paper my own believes become much more pronounced. I discuss and compare the Nazi treatment of Jews and Gypsies; touch upon the most debated and controversial issues and above all analyze the main differences in the treatment of these two groups. Based on the facts from the first chapter and deriving from the discussion in the second chapter I shall then try to draw conclusions concerning Yehuda Bauer s thesis that It does not do any service to the cause of the Romani people to mix them up in the same analytical framework with the Jews by defining the Holocaust as pertaining to both Gypsies and Jews .

Seminar paper from the year 2007 in the subject Politics - Topic: Peace and Conflict, Security, grade: 1, Charles University in Prague, language: English, abstract: The conflict in Darfur has been repeatedly described as one of the worst humanitarian crises the world is facing nowadays. With hundreds of thousands killed and millions more displaced it is still ongoing. In this paper I would like to look at the conflict situation from two perspectives. Firstly, in the first segment of my work, I will try to describe the conflict and its roots as well as explain its origins. For a better understanding I divided this chapter into several sub-chapters dealing with: the background to Darfur; historical roots of the conflict and most importantly with the current conflict focusing on patterns of violence, the actual situation, the IDP camps and sexual violence. In the second half of my paper I tried to look at the conflict from a different perspective, from a perspective of international actors, above all the Western democratic countries in the sub-chapter about the question of genocide and the UN and the AU in the two following sub-chapters. For this paper I used a number of sources, both books and journals or newspaper articles. However, Prunier s book Darfur: The Ambiguous Genocide proved to be the most useful one, since it still is one of the few books dealing precisely with this subject that is available.

Bachelor Thesis from the year 2006 in the subject History of Germany - 1848, Empire, Imperialism, grade: 1, Charles University in Prague, language: English, abstract: In my thesis I examine German colonial policies in South West Africa towards the natives from their first engagement in the area in 1883 up to the end of the Herero war in 1907. Primarily, I try to establish if they were genocidal. ... My thesis is divided into three major parts. The first two describe and characterize the German policies towards the natives of South West Africa and their mutual relationship, prior to the Herero war and during it respectively. The third is concerned with definitions of genocide and relevance for its aplication on the Herero war. In the first chapter I shortly portray South West Africa prior to European colonisation and then turn my attention to German - steady and gradual - conquest of the country. Special consideration is given to German perceptions of the natives, to their use of the natives for their own cause and to their treatment of the indigenous population. Finally the most important aspects of development of the colony under German rule are presented. The next chapter of the thesis deals with the events of the Herero war. Analysis of the main causes of the uprising is followed by the description of the course of war. This one is purposefully not very detailed, and only events relevant for our cause are mentioned. Much more attention is given to German changing policies during the war and to the differing arguments behind these policies, with special focus on Lothar von Trotha's reasoning. The Nama uprising is mentioned briefly as well. At the end results of the war and its influence mainly on the native population are characterized. I deal with the concept of genocide in the final part of this paper. I offer three different definitions and apply them one by one, on the events in Gernam South West Africa at the beginning of the 20th century. I analyze if any, some, or all definitions are valid and could be used to describe these events. The crucial question of this thesis is whether German policies in South West Africa regarding the native population, especially the Herero could be described as genocidal.