We extend the framework of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) operators to derive an energy-conservative and divergence-free scheme for the homogeneous Maxwell\u2019s equations.<\/p>\n
https:\/\/arxiv.org\/abs\/2511.20529v1<\/a><\/p>\n Abstract<\/strong> We extend the framework of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) operators to derive an energy-conservative and divergence-free scheme for the homogeneous Maxwell\u2019s equations. https:\/\/arxiv.org\/abs\/2511.20529v1 Abstract We demonstrate that we can carry over the strategy … Continue reading
\nWe demonstrate that we can carry over the strategy of Finite Element Exterior Calculus (FEEC) to Summation-by-Parts (SBP) Finite Difference (FD) methods to achieve divergence- and curl-free discretizations. This is not obvious at first sight, as for SBP-FD no basis functions are known, but only values and derivatives at points. The key is a remarkable analytic relationship that enables us to construct compatible operators using integral and nodal degrees of freedom. Pre-existing SBP-FD matrix operators can then be used to obtain nodal values from the integral degrees of freedom to derive a scheme with the desired properties.<\/p>\n","protected":false},"excerpt":{"rendered":"