scholarly journals Entropy dissipation of moving mesh adaptation

2014 ◽  
Vol 11 (03) ◽  
pp. 633-653 ◽  
Author(s):  
Mária Lukáčová-Medvid'ová ◽  
Nikolaos Sfakianakis
Keyword(s):  
Numerical Stability ◽  
Sufficient Conditions ◽  
Mesh Adaptation ◽  
Moving Mesh ◽  
Nonlinear Conservation Laws ◽  
The Past ◽  
Entropy Dissipation ◽  
Uniform Grids ◽  
Mesh Reconstruction ◽  
Adaptation Method

Non-uniform grids and mesh adaptation have become an important part of numerical approximations of differential equations over the past decades. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. In this paper we consider nonlinear conservation laws and provide a method to perform the analysis of the moving mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient conditions — on the adaptation of the mesh — that stabilize a numerical scheme in the sense of the entropy dissipation.

A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems

2019 ◽  
Vol 78 (9) ◽  
pp. 2973-2993 ◽  
Author(s):  
Ondřej Bartoš ◽  
Vít Dolejší ◽  
Georg May ◽  
Ajay Rangarajan ◽  
Filip Roskovec
Keyword(s):  
Mesh Adaptation ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Adaptation Method

scholarly journals Mesh Adaptation Method for Optimal Control With Non-Smooth Control Using Second-Generation Wavelet

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 135076-135086
Author(s):  
Zhiwei Feng ◽  
Qingbin Zhang ◽  
Jianquan Ge ◽  
Wuyu Peng ◽  
Tao Yang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Second Generation ◽  
Mesh Adaptation ◽  
Smooth Control ◽  
Second Generation Wavelet ◽  
Adaptation Method

Meshing Method for Transient Computation With Complex Geometry in CFD

2002 ◽  
Author(s):  
J. L. Kueny ◽  
B. Dore´ ◽  
G. Coppens
Keyword(s):  
Complex Geometry ◽  
Mesh Adaptation ◽  
Moving Mesh ◽  
Computational Time ◽  
Tangential Displacement ◽  
Time Step ◽  
Local Observation ◽  
Complex Boundary ◽  
Accuracy Of Results ◽  
Main Ideas

The description of mesh evolution during a transient computation with moving walls and mesh adaptation has to respect many rules. Using a good mesh for each computational time step is important for accuracy of results. The complexity of geometry can make this objective more complex. A method has been developed to obtain a good moving mesh description with complex boundary geometry. It is based on a local observation of boundary movement and can be resumed by two main ideas: • Add cells where the volume of solution domain increases. • Slide the mesh where the boundary has a tangential displacement.

ON THE MATABILITY OF POLYGONS

2008 ◽  
Vol 18 (05) ◽  
pp. 469-506
Author(s):  
GILL BAREQUET ◽  
AYA STEINER
Keyword(s):  
Information Systems ◽  
Medical Imaging ◽  
Surface Reconstruction ◽  
Geographical Information Systems ◽  
Piecewise Linear ◽  
A Priori ◽  
Sufficient Conditions ◽  
Geographical Information ◽  
Triangulated Surface ◽  
The Past

Interpolating a piecewise-linear triangulated surface between two polygons lying in parallel planes has attracted a lot of attention in the literature over the past three decades. This problem is the simplest variant of interpolation between parallel slices, which may contain multiple polygons with unrestricted geometries and/or topologies. Its solution has important applications to medical imaging, digitization of objects, geographical information systems, and more. Practically all currently-known methods for surface reconstruction from parallel slices assume a priori the existence of a non-self-intersecting triangulated surface defined over the vertices of the two polygons, which connects them. Gitlin et al. were the first to specify a nonmatable pair of polygons. In this paper we provide proof of the nonmatability of a “simpler” pair of polygons, which is less complex than the example given by Gitlin et al. Furthermore, we provide a family of polygon pairs with unbounded complexity, which we believe to be nonmatable. We also give a few sufficient conditions for polygon matability.

Brauer Group Analogues of Results Relating the Witt Ring to Valuations and Galois Theory

1995 ◽  
Vol 47 (3) ◽  
pp. 527-543 ◽  
Author(s):  
Yoon Sung Hwangk ◽  
Bill Jacob
Keyword(s):  
Galois Theory ◽  
Sufficient Conditions ◽  
Structure Theory ◽  
Valuation Theory ◽  
Cup Product ◽  
The Past ◽  
Relative Rigidity ◽  
Form Theory ◽  
Special Case ◽  
Adic Case

AbstractLet F be a field of characteristic different from p containing a primitive p-th root of unity. This paper studies the cup product pairing Hl(F, p) x Hl(F, p) → H2(F, p) and its relationship to valuation theory and Galois theory. Sufficient conditions on the pairing which guarantee the existence of a valuation on the field are described. In the non p-adic case these results provide a converse to the well-known structure theory in this situation. In the p-adic case, the pairing is described using the notion of "relative rigidity". These results are analogues of results in quadratic form theory developed in the past decade, which cover the special case p = 2. Applications to the maximal pro-p Galois group of F are also described.

scholarly journals Moving mesh adaptation for Si and GaN-based power device simulation

2018 ◽  
Vol 17 (4) ◽  
pp. 1621-1629
Author(s):  
Fawad Ismail ◽  
Palash Sarker ◽  
Mohamed Mohamed ◽  
Kyekyoon Kim ◽  
Umberto Ravaioli
Keyword(s):  
Device Simulation ◽  
Mesh Adaptation ◽  
Moving Mesh ◽  
Power Device

H THEOREM AND SUFFICIENT CONDITIONS FOR THE DISCRETE VELOCITY DIRECTION MODEL

2012 ◽  
Vol 27 (01) ◽  
pp. 1350007 ◽  
Author(s):  
ZHENYU ZHANG ◽  
CHENG PENG ◽  
JIANZHONG XU
Keyword(s):  
Numerical Stability ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Nonequilibrium State ◽  
Distribution Functions ◽  
Governing Equations ◽  
Discrete Velocity ◽  
Speed Distribution ◽  
H Theorem ◽  
Direction Model

In this paper, we prove that an H theorem exists for the discrete velocity direction model and provide a set of sufficient conditions, in which the speed distribution functions can be both at equilibrium state and at nonequilibrium state in all flow regimes. To enhance the numerical stability, we simplify the governing equations of the discrete velocity direction model by these sufficient conditions and apply these sufficient conditions to boundary conditions and initial conditions.

Time Dependent Calculations for Incompressible Flows on Adaptive Unstructured Meshes

2003 ◽  
Author(s):  
Xiang Zhao ◽  
Jun Wang ◽  
Sijun Zhang
Keyword(s):  
Large Scale ◽  
Incompressible Flows ◽  
Computational Cost ◽  
Mesh Adaptation ◽  
Time Dependent ◽  
Reynolds Number Flow ◽  
Viscous Incompressible Flows ◽  
Number Flow ◽  
Time Dependent Problems ◽  
Adaptation Method

An adaptive unstructured method has been developed for simulating two-dimensional unsteady, viscous, incompressible flows. The pressure-based approach coupled with a mesh adaptation method is employed to better capture the details of flow physics for time dependent problems by optimizing computational cost with respect to accuracy. The mesh adaptation for locally refining and coarsening hybrid unstructured grid is based on hanging node approach. The time dependent calculations is further enhanced by virtue of parallel computing which is the most powerful for large scale intensive computation at the present time. The proposed method is validated by comparison with experimental results of low Reynolds number flow over a shedding circular cylinder.

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