# 101.A14 AKNUM Boundary Element Methods This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2023W

2023W, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Presence

## Learning outcomes

After successful completion of the course, students are able to formulate certain partial differential equations as equivalent integral equations. They can discretize these equations via a Galerkin method and understand the underlying mathematical theory.

## Subject of course

Classical numerical algorithms, like the finite element method, is based on decomposing the underlying domain of interest and solve a discretized version of the partial differential equation on these pieces. An alternative approach is to reformulate the problem as an equivalent integral equation on the boundary of the domain using the fundamental solution. Once reformulated, the problem can then be discretized using a Galerkin method.

This approach has multiple advantages:

1) reduction of dimension: instead of  a 2d domain, only  a 1d curve has to be discretized

2) unbounded domains can also be considered

3) better convergence rates compared to finite elment methods

This lecture introduces the theory of boundary element methods (BEM). It lays the mathematical foundation as well as deals with more practical aspects of the method.

Topics include:

- derivation of the representation formula and integral equations

- a priori convergence theory

- assembly of the stiffness matrix and numerical quadrature for singular integrals

- matrix compression techniques, e.g. using H-matrices

## Teaching methods

Blackboard lecture

## Mode of examination

Oral

The exact date and time for the lecture will be discussed and specified in the first lecture.

## Course dates

DayTimeDateLocationDescription
Thu14:00 - 15:0005.10.2023 Seminar room DA grün 03 CInitial meeting
Wed14:00 - 15:3011.10.2023 - 24.01.2024 Seminar room DA grün 03 CLecture
AKNUM Boundary Element Methods - Single appointments
DayDateTimeLocationDescription
Thu05.10.202314:00 - 15:00 Seminar room DA grün 03 CInitial meeting
Wed11.10.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed18.10.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed25.10.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed08.11.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed22.11.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed29.11.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed06.12.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed13.12.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed20.12.202314:00 - 15:30 Seminar room DA grün 03 CLecture
Wed10.01.202414:00 - 15:30 Seminar room DA grün 03 CLecture
Wed17.01.202414:00 - 15:30 Seminar room DA grün 03 CLecture
Wed24.01.202414:00 - 15:30 Seminar room DA grün 03 CLecture

Oral exam

Not necessary

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Mandatory elective

## Literature

No lecture notes are available.

## Previous knowledge

Numerical analyis, partial differential equations.

Experience with finite element methods is helpful.

## Language

if required in English