Explicit geometric construction of sparse inverse mass matrices for arbitrary tetrahedral grids

Pitassi, Silvano; Trevisan, F.; Specogna, Ruben

doi:10.1016/j.cma.2021.113699

Cited by 3 publications

(2 citation statements)

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“…Remark 1. Note that the definition of P 0 -consistency involves only the local projection matrices, as in (4), that collect local face vectors, as defined in (3).…”

Section: Curved Mfd Methodsmentioning

confidence: 99%

“…As a second approach, we can interpolate with standard least squares methods face DoFs inside each element to produce a constant vector field. Then, the mass matrix is obtained by projecting the constant vector field onto edges of a dual (or secondary) grid K [3]. A dual grid K is constructed by duality starting from a given discretization grid K, hence, called a primal grid.…”

Section: Introductionmentioning

confidence: 99%

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The curved Mimetic Finite Difference method: allowing grids with curved faces

Pitassi¹,

Igor²,

Trevisan³

et al. 2022

Preprint

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We present a new mimetic finite difference method able to deal with curved faces.Notably, it yields a symmetric discrete problem which uses only one degree of freedom for each curved face. The principle at the core of our construction is to abandon the standard definition of local consistency of mimetic finite difference methods. Instead, we exploit the novel and global concept of P 0 -consistency.Numerical examples confirm the consistency and the convergence of the method for real-case problems with curved boundary geometries.

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“…Remark 1. Note that the definition of P 0 -consistency involves only the local projection matrices, as in (4), that collect local face vectors, as defined in (3).…”

Section: Curved Mfd Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%