Robust Zero-Change Self-Configuration of the Rectangular Mesh

2021 ◽  
Author(s):  
Ryan Hamerly ◽  
Saumil Bandyopadhyay ◽  
Dirk Englund
Keyword(s):  
Rectangular Mesh

scholarly journals Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures

2017 ◽  
Vol 21 (3) ◽  
pp. 835-866 ◽  
Author(s):  
Meng Wu ◽  
Bernard Mourrain ◽  
André Galligo ◽  
Boniface Nkonga
Keyword(s):  
Isogeometric Analysis ◽  
Convergence Rates ◽  
Approximation Order ◽  
Basis Functions ◽  
Physical Domain ◽  
Piecewise Polynomial ◽  
Numerical Convergence ◽  
Rectangular Mesh ◽  
Piecewise Polynomial Functions ◽  
Potential Applications

AbstractMotivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric analysis, we present splines defined over a rectangular mesh with a complex topological structure, i.e., with extraordinary vertices. These splines are piecewise polynomial functions of bi-degree (d,d) and parameter continuity. And we compute their dimension and exhibit basis functions called Hermite bases for bicubic spline spaces. We investigate their potential applications for solving partial differential equations (PDEs) over a physical domain in the framework of Isogeometric analysis. For instance, we analyze the property of approximation of these spline spaces for the L2-norm; we show that the optimal approximation order and numerical convergence rates are reached by setting a proper parameterization, although the fact that the basis functions are singular at extraordinary vertices.

scholarly journals A Study on the accuracy of finite volume numerical models with non-rectangular mesh

2021 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
M. Morovvat ◽  
A. R. Zarrati ◽  
M. R. Jalili-Ghazizadeh
Keyword(s):  
Finite Volume ◽  
Numerical Models ◽  
Rectangular Mesh

Assembling of Parallel Programs for Large Scale Numerical Modeling

2012 ◽  
pp. 497-511
Author(s):  
V.E. Malyshkin
Keyword(s):  
Large Scale ◽  
Parallel Implementation ◽  
Numerical Models ◽  
Dynamic Properties ◽  
Parallel Program ◽  
Particle In Cell ◽  
Modular Programming ◽  
Rectangular Mesh ◽  
Assembly Technology ◽  
Main Ideas

The main ideas of the Assembly Technology (AT) in its application to parallel implementation of large scale realistic numerical models on a rectangular mesh are considered and demonstrated by the parallelization (fragmentation) of the Particle-In-Cell method (PIC) application to solution of the problem of energy exchange in plasma cloud. The implementation of the numerical models with the assembly technology is based on the construction of a fragmented parallel program. Assembling of a numerical simulation program under AT provides automatically different useful dynamic properties of the target program including dynamic load balance on the basis of the fragments migration from overloaded into underloaded processor elements of a multicomputer. Parallel program assembling approach also can be considered as combination and adaptation for parallel programming of the well known modular programming and domain decomposition techniques and supported by the system software for fragmented programs assembling.

Localization Effects in Bammann-Chiesa-Johnson Metals With Damage Delocalization

2011 ◽  
Author(s):  
Koffi Enakoutsa ◽  
Fazle R. Ahad ◽  
Kiran N. Solanki ◽  
Yustianto Tjiptowidjojo ◽  
Douglas J. Bammann
Keyword(s):  
Velocity Gradient ◽  
Adiabatic Shear Band ◽  
Shear Banding ◽  
Material Model ◽  
Dissipated Energy ◽  
Dissipation Energy ◽  
Plane Strain Tension ◽  
Nonlocal Evolution Equation ◽  
Rectangular Mesh ◽  
Spatial Discontinuity

The presence of softening in the Bammann-Chiesa-Johnson (BCJ) material model presents a major physical drawback: the unlimited localization of strain which results in spurious zero dissipated energy at failure. This difficulty resolves when the BCJ model is modified to incorporate a nonlocal evolution equation for the damage, as proposed by Pijaudier-Cabot and Bazant (1987). The objective of this work is to theoretically assess the ability of such a modified BCJ model to prevent unlimited localization of the strain. To that end, we investigate two localization problems in nonlocal BCJ metals: appearance of a spatial discontinuity of the velocity gradient in a finite, inhomogeneous body, and localization into finite bands. We show that in spite of the softening arising from the damage, no spatial discontinuity occurs in the velocity gradient. Also, we find that the dissipation energy is continuously distributed in nonlocal BCJ metals and therefore can not localize into zones of vanishing volume. As a result, the appearance of any vanishing width adiabatic shear band is impossible in a nonlocal BCJ metal. Finally, we study the finite element (FE) solution of shear banding in a rectangular mesh, deformed in plane strain tension and containing an imperfection, thereby illustrating the effects of imperfections on the localization of the strain.

scholarly journals Murray’s law for discrete and continuum models of biological networks

2019 ◽  
Vol 29 (12) ◽  
pp. 2359-2376
Author(s):  
Jan Haskovec ◽  
Peter Markowich ◽  
Giulia Pilli
Keyword(s):  
Biological Networks ◽  
Discrete Model ◽  
Continuum Model ◽  
Transportation Network ◽  
Continuum Models ◽  
Scaling Relation ◽  
Murray's Law ◽  
Murray’S Law ◽  
Rectangular Mesh ◽  
The Continuum

We demonstrate the validity of Murray’s law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray’s law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray’s law for its linearly stable steady states.

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