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We present a framework for the structure-preserving approximation of partialdifferential equations on mapped multipatch domains, extending the classicaltheory of finite element exterior calculus (FEEC) to discrete de Rham sequenceswhich are broken, i.e., fully discontinuous across the patch interfaces.Following the Conforming/Nonconforming Galerkin (CONGA) schemes developed in[http://dx.doi.org/10.1090/mcom/3079, arXiv:2109.02553, our approach is basedon: (i) the identification of a conforming discrete de Rham sequence withstable commuting projection operators, (ii) the relaxation of the continuityconstraints between patches, and (iii) the construction of conformingprojections mapping back to the conforming subspaces, allowing to definediscrete differentials on the broken sequence.  This framework combines the advantages of conforming FEEC discretizations(e.g. commuting projections, discrete duality and Hodge-Helmholtzdecompositions) with the data locality and implementation simplicity ofinterior penalty methods for discontinuous Galerkin discretizations. We applyit to several initial- and boundary-value problems, as well as eigenvalueproblems arising in electromagnetics. In each case our formulations are shownto be well posed thanks to an appropriate stabilization of the jumps across theinterfaces, and the solutions are extremely robust with respect to thestabilization parameter.  Finally we describe a construction using tensor-product splines on mappedcartesian patches, and we detail the associated matrix operators. Our numericalexperiments confirm the accuracy and stability of this discrete framework, andthey allow us to verify that expected structure-preserving properties such asdivergence or harmonic constraints are respected to floating-point accuracy.

A broken FEEC framework for electromagnetic problems on mapped multipatch domains