Application of complementary formulations and adaptive mesh refinements to non-linear magnetostatic problems

1995 ◽  
Vol 31 (3) ◽  
pp. 1376-1379 ◽  
Author(s):  
Chengjun Li ◽  
Zhuoxiang Ren ◽  
A. Razek
Keyword(s):  
Adaptive Mesh ◽  
Non Linear ◽  
Mesh Refinements

Computation of Composite Strengths by Limit Analysis

2019 ◽  
Vol 810 ◽  
pp. 137-142 ◽  
Author(s):  
Stanislav Sysala ◽  
Radim Blaheta ◽  
Alexej Kolcun ◽  
Jiří Ščučka ◽  
Kamil Souček ◽  
...  
Keyword(s):  
Limit Analysis ◽  
Laboratory Experiments ◽  
Optimization Problem ◽  
Adaptive Mesh ◽  
Hard Coal ◽  
Semismooth Newton Method ◽  
Analysis Problem ◽  
Semismooth Newton ◽  
Higher Order Finite Elements ◽  
Mesh Refinements

The paper is focused on computation of a compressive strength of composite materials by limit analysis. This method enables to determine the strength or other types of limit loads by solution of a specific optimization problem. It is also capable to predict failure zones. Abilities of the method are investigated on a particular composite -- a laboratory prepared sample consisting of a hard coal matrix and a polyurethane binder. This sample is chosen due to available CT images of the inner structure and laboratory experiments. Appropriate yield criteria are proposed for the coal and the binder in order to define the limit analysis problem. This problem is penalized and then discretized by higher order finite elements. For numerical solution, the semismooth Newton method and adaptive mesh refinements are also used. Numerical experiments in 2D for various CT scans and material parameters are performed.

scholarly journals Convergence of SPH and AMR simulations

2010 ◽  
Vol 6 (S270) ◽  
pp. 429-432
Author(s):  
David A. Hubber ◽  
Sam A. E. G. Falle ◽  
Simon P. Goodwin
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Thin Shell ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Helmholtz Instability ◽  
Non Linear ◽  
Particle Hydrodynamics ◽  
First Results ◽  
Order Of Magnitude ◽  
Smoothed Particle

AbstractWe present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

Numerical Wave Tanks Based on Finite Element and Boundary Element Modelling

2005 ◽  
Author(s):  
R. Eatock Taylor ◽  
G. X. Wu ◽  
W. Bai ◽  
Z. Z. Hu
Keyword(s):  
Finite Element ◽  
Boundary Element ◽  
Adaptive Mesh ◽  
Element Model ◽  
The Body ◽  
Test Cases ◽  
Fe Model ◽  
Linear Interaction ◽  
Adaptive Mesh Generation ◽  
Non Linear

This work forms part of an investigation into the non-linear interaction between steep transient waves and flared structures, using a coupled finite element and boundary element model. The use of a coupled approach is based on consideration of the relative strengths and weaknesses of the finite element (FE) and boundary element (BE) methods when implemented separately (e.g. efficiency of computation versus complexity of adaptive mesh generation). An FE model can be used to advantage away from the body, where the domain is regular, and a BE discretisation near the body where the moving mesh is complex. The paper describes aspects of the FE and BE models which have been developed for this analysis, each based on the use of quadratic isoparametric elements implemented in a mixed Eulerian-Lagrangian formulation. Initially the two approaches have been developed side by side, in order to ensure the use of robust components in the coupled formulation. Results from these methods are obtained for a series of test cases, including the interaction of an impulse wave with a circular cylinder in a circular tank, and non-linear diffraction by a cylinder in a long tank.

Adaptive Mesh Refinement in 2D – An Efficient Implementation in Matlab

2020 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Stefan A. Funken ◽  
Anja Schmidt
Keyword(s):  
Data Structure ◽  
Adaptive Mesh Refinement ◽  
Numerical Experiments ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Two Dimensions ◽  
Efficient Implementation ◽  
Research And Education ◽  
Mesh Refinements ◽  
Implementation In Matlab

AbstractThis paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.

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