Mimetic finite difference methods for diffusion equations

J Hyman, J Morel, M Shashkov, S Steinberg - Computational Geosciences, 2002 - Springer
This paper reviews and extends the theory and application of mimetic finite difference
methods for the solution of diffusion problems in strongly heterogeneous anisotropic …

Numerical modeling of heat-transfer and the influence of process parameters on tailoring the grain morphology of IN718 in electron beam additive manufacturing

N Raghavan, R Dehoff, S Pannala, S Simunovic… - Acta Materialia, 2016 - Elsevier
The fabrication of 3-D parts from CAD models by additive manufacturing (AM) is a disruptive
technology that is transforming the metal manufacturing industry. The correlation between …

Localized melt-scan strategy for site specific control of grain size and primary dendrite arm spacing in electron beam additive manufacturing

N Raghavan, S Simunovic, R Dehoff, A Plotkowski… - Acta Materialia, 2017 - Elsevier
In addition to design geometry, surface roughness, and solid-state phase transformation,
solidification microstructure plays a crucial role in controlling the performance of additively …

The RAGE radiation-hydrodynamic code

M Gittings, R Weaver, M Clover, T Betlach… - … Science & Discovery, 2008 - iopscience.iop.org
We describe RAGE, the'radiation adaptive grid Eulerian'radiation-hydrodynamics code,
including its data structures, its parallelization strategy and performance, its hydrodynamic …

A family of mimetic finite difference methods on polygonal and polyhedral meshes

F Brezzi, K Lipnikov, V Simoncini - Mathematical Models and …, 2005 - World Scientific
A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL
MESHES | Mathematical Models and Methods in Applied Sciences World Scientific Search …

Robust approximate inverse preconditioning for the conjugate gradient method

M Benzi, JK Cullum, M Tuma - SIAM Journal on Scientific Computing, 2000 - SIAM
We present a variant of the AINV factorized sparse approximate inverse algorithm which is
applicable to any symmetric positive definite matrix. The new preconditioner is breakdown …

Beyond flux-limited diffusion: parallel algorithms for multidimensional radiation hydrodynamics

JC Hayes, ML Norman - The Astrophysical Journal Supplement …, 2003 - iopscience.iop.org
This paper presents a new code for performing multidimensional radiation hydrodynamic
(RHD) simulations on parallel computers involving anisotropic radiation fields and …

Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes

K Lipnikov, J Morel, M Shashkov - Journal of Computational Physics, 2004 - Elsevier
Mimetic finite difference methods for diffusion equations on non-orthogonal non-conformal meshes
- ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & Books Search …

Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces

F Brezzi, K Lipnikov, M Shashkov - Mathematical Models and …, 2006 - World Scientific
New mimetic finite difference discretizations of diffusion problems on unstructured
polyhedral meshes with strongly curved (non-planar) faces are developed. The material …

Accurate two-phase flow simulation in faulted reservoirs by combining two-point flux approximation and mimetic finite difference methods

R Dong, FO Alpak, MF Wheeler - SPE Journal, 2023 - onepetro.org
Faulted reservoirs are commonly modeled by corner-point grids (CPGs). Because the two-
point flux approximation (TPFA) method is not consistent on non-K-orthogonal grids, multi …