This course aims at giving the mathematical foundations for the study of partial differential equations posed in an unbounded domain. We will focus on model equations (Laplace, Helmholtz, wave equation) to present the mathematical framework and the main ideas for the design of numerical methods.
Propagation phenomena. Partial differential equations. Unbounded domains.
Part I : Basic facts for stationary and harmonic problems
Part II : Time dependent problems
Part III : Focus on the Helmholtz problem in the free space
- To be able to identify conditions for closing a problem in an unbounded domain.
- To be able to design a numerical method for PDEs in unbounded domains.
- To be able to quantify the accuracy of such a numerical method.
Grade = 50% knowledge + 50% knowhow Knowledge grade = 100% final exam Knowhow grade = 100% continuous assessment