Magic formulas are the geometric identities at the root of modern compatible schemes for polyhedral grids. We present rigorous yet elementary proofs of the magic formulas originating from Stokes theorem. The proofs enlighten new fundamental aspects of the mass matrices produced with the magic formulas. First, the construction of the mass matrices works for an unexpectedly broad type of mesh cells. Second, they show that dual nodes can be arbitrarily positioned thus extending the construction of the dual barycentric grid.
New Magic Formula Demonstration Shows Unexpected Features of Geometrically Defined Matrices for Polyhedral Grids / Pitassi, S.; Ghiloni, R.; Specogna, R.. - In: IEEE TRANSACTIONS ON MAGNETICS. - ISSN 0018-9464. - STAMPA. - 57:6(2021). [10.1109/TMAG.2021.3067438]
New Magic Formula Demonstration Shows Unexpected Features of Geometrically Defined Matrices for Polyhedral Grids
Ghiloni R.;
2021-01-01
Abstract
Magic formulas are the geometric identities at the root of modern compatible schemes for polyhedral grids. We present rigorous yet elementary proofs of the magic formulas originating from Stokes theorem. The proofs enlighten new fundamental aspects of the mass matrices produced with the magic formulas. First, the construction of the mass matrices works for an unexpectedly broad type of mesh cells. Second, they show that dual nodes can be arbitrarily positioned thus extending the construction of the dual barycentric grid.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
