Dual mesh approach for semiconductor device simulator

Kojima, Takeshi; Saito, Yoshifuru; Dang, Ryo

doi:10.1109/20.34335

Cited by 2 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the Yee's FDTD scheme, this is achieved by the dual orthogonal hexahedral grid construction. For an arbitrary simplicial lattice, however, this is not possible in general (some particular tetrahedral and dual grid constructions, such as the Delaunay-Voronoi grid [46], are mutually orthogonal by construction and therefore produce diagonal Hodge operators at the expense geometric flexibility). In general, the matrices in Eqs.…”

Section: Discrete Hodge Operatorsmentioning

confidence: 99%

“…This non-locality turns out to be a general feature in the case of arbitrary (non-orthogonal) lattices. Diagonal matrices are obtained only in particular cases by an explicit construction of orthogonal dual lattices (such as the Yee cell [54][55][56][57][58][59][60][61] or the Voronoi-Delaunay cell mentioned before [46,61,62]). A similar non-local character is also present (this time on the definition of discrete spatial operators or their adjoints) in discretization schemes which do not resort to a dual lattice construction [63][64][65].…”

Section: Whitney Maps On the Dual Lattice Via Barycentric Subdivisionmentioning

confidence: 99%

See 1 more Smart Citation

Geometric Aspects of the Simplicial Discretization of Maxwell's Equations

Teixeira¹

2001

PIER

View full text Add to dashboard Cite

Abstract-Aspects of the geometric discretization of electromagnetic fields on simplicial lattices are considered. First, the convenience of the use of exterior differential forms to represent the field quantities through their natural role as duals (cochains) of the geometric constituents of the lattice (chains = nodes, edges, faces, volumes) is briefly reviewed. Then, the use of the barycentric subdivision to decompose the (ordinary) simplicial primal lattice together with the (twisted) non-simplicial barycentric dual lattice into simplicial elements is considered. Finally, the construction of lattice Hodge operators by using Whitney maps on the first barycentric subdivision is described. The objective is to arrive at a discrete formulation of electromagnetic fields on general lattices which better adheres to the underlying physics.

show abstract

Section: Discrete Hodge Operatorsmentioning

confidence: 99%