1 research outputs found
Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM
Elliptic boundary value problems which are posed on a random domain can be
mapped to a fixed, nominal domain. The randomness is thus transferred to the
diffusion matrix and the loading. While this domain mapping method is quite
efficient for theory and practice, since only a single domain discretisation is
needed, it also requires the knowledge of the domain mapping.
However, in certain applications, the random domain is only described by its
random boundary, while the quantity of interest is defined on a fixed,
deterministic subdomain. In this setting, it thus becomes necessary to compute
a random domain mapping on the whole domain, such that the domain mapping is
the identity on the fixed subdomain and maps the boundary of the chosen fixed,
nominal domain on to the random boundary.
To overcome the necessity of computing such a mapping, we therefore couple
the finite element method on the fixed subdomain with the boundary element
method on the random boundary. We verify the required regularity of the
solution with respect to the random domain mapping for the use of multilevel
quadrature, derive the coupling formulation, and show by numerical results that
the approach is feasible