Some recent developments in solving PDEs in unbounded domains by Inverted finite element methods
The modelling of various phenomena in physics and in engineering leads to partial differential equations in unbouded geometrical domains. The analysis of these PDEs and the approximation of their solutions necessitate a special treatment of the behavior of functions at large distances. Moreover, regardless of the method used, the accuracy and the reliability of the approximation is in general strongly depending on the manner in which this asymptotic behavior is taken into account.
The main objective of this talk is to provide a general overview of the Inverted finite element method (IFEM). The IFEM is a non truncation method which can easily be adapted to multidimensional elliptic problems.
Its advantages include:
- (a) the preservation of the unboundness of the domain
- (b) the possibility to tackle equations having varying coefficients at large distances
- (c) a high degree of flexibility
We will in particular show how the method can be used for solving some problems arising in physics (especially in fluid mechanics,in quantum chemistry and in quantum physics). Recent 1D, 2D and 3D
computational results will be presented.