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We present an implicit coupling algorithm that is suitable for strongly coupled
physical problems that were discretized by heterogeneous numerical schemes,
namely finite volume and finite element methods. The primary characteristic
of the proposed scheme is an implicit treatment of the heterogeneous schemes
through a single matrix approach. The finite element and finite volume parts of
the discretized domain exchange information through a coupling boundary and
the resulting discretization coefficients are stored in a block matrix. The structure
of the matrix is such that the coupling coefficients are stored in the off-diagonal
blocks of the matrix, while finite element and finite volume subdomains are stored
in the diagonal blocks of the matrix. A suite of efficient linear solvers based on the
Krylov subspace methods were developed for the solution of the resulting coupling
problem. Several demonstration cases that illustrate the coupling algorithm are
presented.