Institut für Angewandte Mathematik

Lecture in winter term 2020/2021 
Numerical Mathematics 4 / Elective subject mathematics (Boundary Element Methods) 
Content 
Boundary element methods are suitable for the approximate solution of partial differential equations. An advantage of the boundary element methods is that only the surface of the considered body has to be meshed.
We start with a brief introduction of boundary integral equations.
For the boundary element methods, the discretization of the boundary integral equations is discussed for the approximate solution of the boundary integral equations and the underlying boundary value problem. Thereby several theoretical aspects are investigated and illustrated by numerical examples.

Previous knowledge expected 
Computational Mathematics 3, Partial Differential Equations

Scheduled dates 
 Mondays, 16:1518:00, seminar room STEG006
 Fridays, 10:1511:45, seminar room STEG006
 Scheduled dates: TUG Online
 first lecture: October 2, 2020

Exam 
 oral exam by arrangement
 Due to study directives the language of presentation is English.

Exercise course 
 Exam method and evaluation of the exercise course:
 There will probably be 3 exercise sheets with calculation examples and 3 exercise sheets with coding examples.
 The students have to mark (votieren) the calculation examples they were able to solve at the beginning of each class. The students can be asked to present any example marked as solved on the blackboard. Due to study directives the language of presentation is English.
The percentage of marked examples will account for 25 % of the total number of points.
 The particpants have to present at least two calculation examples succesfully. The quality of the presentations will account for 25 % of the total number of points.
 The solutions of the coding examples have to be submitted. Each coding exercise sheet accounts for approximately 1/6 of the total number of points.
 50 % of the total number of points are sufficient to pass the exam.
 After voting or submission for two exam dates the course will be assessed negatively if applicable.
 Fridays, 10:1512:00, seminar room STEG006
 Scheduled dates: TUG Online

Selected References 
 Olaf Steinbach.
Numerical Approximation Methods for Elliptic Boundary Value Problems.
Finite and Boundary Elements.
Springer, New York, 2008.
 Stefan A. Sauter and Christoph Schwab.
Boundary element methods, volume 39 of Springer Series in
Computational Mathematics.
SpringerVerlag, Berlin, 2011.
 Joachim Gwinner and Ernst Peter Stephan.
Advanced Boundary Element Methods, volume 52 of Springer Series in Computational Mathematics.
Springer, Cham, 2018.
 William McLean.
Strongly elliptic systems and boundary integral equations..
Cambridge: Cambridge University Press, 2000.
 George C. Hsiao and Wolfgang L. Wendland.
Boundary integral equations, volume 164 of Applied Mathematical
Sciences. SpringerVerlag, Berlin, 2008.
 Sergej Rjasanow and Olaf Steinbach.
The Fast Solution of Boundary Integral Equations.
Mathematical and Analytical Techniques with Applications to Engineering.
Springer, New York, 2007.

Contact 
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