The open-source library preCICE enables the creation of partitioned multi-physics simu-
lations where different solvers run independently and exchange coupling data, such as
forces, displacements or heat fluxes.
These differents solvers all use their own space discretization, which usually leads to non-
matching meshes. Coupling these codes requires some form of data mapping of physical
quantites from a mesh to another.
preCICE offers different mapping methods, varying in accuracy, cost, and access to solver
internals (such as derivatives or mesh topology). One of them uses mesh connectivity to
project the points of one mesh into the other mesh and to use construct a piecewise lin-
ear interpolant. However, this projection method was designed for surface coupling: each
mesh used by preCICE represents the boundary of a solver’s domain.
preCICE can also be used for volumetric coupling, where data is exchanged on the whole
domain and not only at the boundary. In this context, projection-based mapping can’t be
used in its current implementation, as it assumes the mesh represents a boundary and not
the domain. This thesis proposes a new data mapping method adapted for volumetric
coupling, using mesh connectivity to build a piecewise linear interpolant over the whole
domain instead of a coupling boundary. It is mathematically derived, implemented in
preCICE and compared to other available methods. Finally, new preCICE tutorials are de-
signed to showcase its use in coupled simulations.