MAPVAR - A Computer Program to Transfer Solution Data Between Finite Element Meshes

Wellman, Gerald W.

doi:10.2172/4162

Cited by 12 publications

(15 citation statements)

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“…Solution variables were mapped from the old mesh to the new mesh using MAPVAR (a Sandia-developed utility computer program, see Wellman 1999). We automated the process of re-meshing and remapping using a Unix script.…”

Section: Numerical Solution Methods Re-meshing and Re-mappingmentioning

confidence: 99%

Multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates.

Chen¹

2004

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This report documents the author's efforts in the deterministic modeling of coppersulfidation corrosion on non-planar substrates such as diodes and electrical connectors. A new framework based on Goma was developed for multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates. In this framework, the moving sulfidation front is explicitly tracked by treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and repeatedly performing re-meshing using CUBIT and re-mapping using MAPVAR. Three one-dimensional studies were performed for verifying the framework in asymptotic regimes. Limited model validation was also carried out by comparing computed copper-sulfide thickness with experimental data. The framework was first demonstrated in modeling one-dimensional copper sulfidation with charge separation. It was found that both the thickness of the space-charge layers and the electrical potential at the sulfidation surface decrease rapidly as the Cu 2 S layer thickens initially but eventually reach equilibrium values as Cu 2 S layer becomes sufficiently thick; it was also found that electroneutrality is a reasonable approximation and that the electro-migration flux may be estimated by using the equilibrium potential difference between the sulfidation and annihilation surfaces when the Cu 2 S layer is sufficiently thick. The framework was then employed to model copper sulfidation in the solid-state-diffusion controlled regime (i.e. stage II sulfidation) on a prototypical diode until a continuous Cu 2 S film was formed on the diode surface. The framework was also applied to model copper sulfidation on an intermittent electrical contact between a gold-plated copper pin and gold-plated copper pad; the presence of Cu 2 S was found to raise the effective electrical resistance drastically. Lastly, future research needs in modeling atmospheric copper sulfidation are discussed.

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Section: Numerical Solution Methods Re-meshing and Re-mappingmentioning

confidence: 99%

Multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates.

Chen¹

2004

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“…Re-meshing was performed every 10-20 time steps (depending on process conditions and proximity of the deposition surface to the top of the trench) using CUBIT [4]. Solution variables were mapped from the old mesh to the new one using a utility program MAPVAR [5]. The process of re-meshing and remapping is automated with a Unix script.…”

Section: 8mentioning

confidence: 99%

Two-dimensional modeling of nickel electrodeposition in LIGA microfabrication

Chen

Evans

2004

Microsystem Technologies

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Two-dimensional processes of nickel electrodeposition in LIGA microfabrication were modeled using the finite-element method and a fully coupled implicit solution scheme via Newton's technique. Species concentrations, electrolyte potential, flow field, and positions of the moving deposition surfaces were computed by solving the species-mass, charge, and momentum conservation equations as well as pseudo-solid mesh-motion equations that employ an arbitrary Lagrangian-Eulerian (ALE) formulation. Coupling this ALE approach with repeated re-meshing and re-mapping makes it possible to track the entire transient deposition processes from start of deposition until the trenches are filled, thus enabling the computation of local current densities that influence the microstructure and functional/mechanical properties of the deposit. IntroductionElectroforming or electrodeposition is a key process in LIGA microfabrication. The process involves multidimensional, transient phenomena that include metalreduction electrochemical reactions on moving deposition surfaces and transport of charged and neutral species via diffusion, electro-migration, and convection in a centimeter-scale electrolyte-bath region and in micron-scale feature trenches. Computational modeling can help in the understanding of these complex, coupled phenomena and aid in elucidating the mechanisms involved. Specifically, by computing local current densities along the moving deposition surfaces, one can relate deposit microstructure (which controls the functional and mechanical properties of the structure) to process conditions (e.g., applied current load, bath composition, pH, and temperature) and trench geometries (widths, aspect ratios), provided that constitutive models relating current density to microstructure (e.g., grain size and orientation) and microstructure to functional/mechanical properties are available.Pioneering work was carried out by Griffiths et al.[1], who developed one and two-dimensional numerical models describing electrodeposition of metal into high aspect-ratio molds. Their one-dimensional model describes dissociation, diffusion, electromigration, and deposition of multiple ionic species; their two-dimensional model focuses on single-species transport including forced flow due to bath stirring and buoyancyinduced natural convection due to density variations. However, transient and moving boundary effects were neglected in that study. Recently, we developed and demonstrated a multi-dimensional framework for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electrochemical reactions on moving deposition surfaces [2]. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation for the electrolyte potential was derived. By treating the finite-element mesh as a pseudo solid and by employing repeated re-meshing (the process of generating a new finite-element mesh for the computational domain) and re-mapping (the process...

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“…The mesh can then be improved, remeshed or modiÿed within the mesh generation toolkit environment, while maintaining any applied boundary conditions to the elements. The new elements can then be exported, any analysis variables associated with the model mapped to the new mesh [19], and the analysis continued. Ideally this procedure should be automated so that no user intervention is required to remesh and restart the analysis.…”

Section: Examplesmentioning

confidence: 99%

Mesh‐based geometry

Owen

White

2003

Numerical Meth Engineering

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SUMMARYA systematic approach to building a complete geometric and topologic representation of a model given only the ÿnite element (FE) description is proposed. The objective of the proposed system is to provide a geometry foundation for existing ÿnite element based models so that standard mesh generation tools can be used without requiring CAD-based modelling systems such as ACIS or other proprietary commercial tools. To accomplish this, a method for extracting topology from the FE model is proposed. Topology entities including volumes, surfaces, curves and vertices are built based on user-deÿned boundary conditions and surface features. Curve and surface geometry is described by either linear triangular facets or G 1 continuous 4th-order Bezier patches. Integration of the proposed mesh-based geometry (MBG) system into an existing mesh generation toolkit is described. Sample applications and examples of MBG are presented. Published in

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MAPVAR - A Computer Program to Transfer Solution Data Between Finite Element Meshes

Cited by 12 publications

References 0 publications

Multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates.

Multi-dimensional modeling of atmospheric copper-sulfidation corrosion on non-planar substrates.

Two-dimensional modeling of nickel electrodeposition in LIGA microfabrication

Mesh‐based geometry

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