scholarly journals A level-set approach for inverse problems involving obstacles Fadil SANTOSA

1996 ◽  
Vol 1 ◽  
pp. 17-33 ◽  
Author(s):  
Fadil Santosa
Keyword(s):  
Inverse Problems ◽  
Level Set ◽  
Level Set Approach

scholarly journals On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
A. De Cezaro
Keyword(s):  
Inverse Problems ◽  
Level Set Method ◽  
Level Set ◽  
Regularization Method ◽  
Level Sets ◽  
Approximate Solutions ◽  
Type Method ◽  
Ill Posed ◽  
Level Set Approach ◽  
Level Set Framework

We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level-set method in some interesting inverse problems arising in elliptic PDE models.

Two-phase flow stability analysis using a level set approach

2017 ◽  
Author(s):  
Mamta Raju Jotkar ◽  
Daniel Rodriguez ◽  
Bruno Marins Soares
Keyword(s):  
Stability Analysis ◽  
Level Set ◽  
Two Phase Flow ◽  
Flow Stability ◽  
Phase Flow ◽  
Two Phase ◽  
Level Set Approach

Hydrodynamic simulation of air bubble implosion using a level set approach

2006 ◽  
Vol 215 (1) ◽  
pp. 98-132 ◽  
Author(s):  
Sunitha Nagrath ◽  
Kenneth Jansen ◽  
Richard T. Lahey ◽  
Iskander Akhatov
Keyword(s):  
Level Set ◽  
Hydrodynamic Simulation ◽  
Air Bubble ◽  
Level Set Approach

Modeling of discrete intersecting discontinuities in rock mass using XFEM/level set approach

2016 ◽  
pp. 239-246
Author(s):  
Kamal Das ◽  
Sandeep Sandha ◽  
Eduardo Rodrigues ◽  
U Mello ◽  
Ignacio Carol ◽  
...  
Keyword(s):  
Rock Mass ◽  
Level Set ◽  
Level Set Approach

Numerical Modelling of Plastic Deformation and Subsequent Recrystallization in Polycrystalline Materials, Based on a Digital Material Framework

2007 ◽  
Vol 558-559 ◽  
pp. 1133-1138 ◽  
Author(s):  
Roland E. Logé ◽  
M. Bernacki ◽  
H. Resk ◽  
H. Digonnet ◽  
T. Coupez
Keyword(s):  
Level Set ◽  
Large Strain ◽  
Voronoi Tessellation ◽  
Constitutive Law ◽  
Polycrystalline Materials ◽  
Large Strains ◽  
Element Mesh ◽  
Digital Material ◽  
Digital Sample ◽  
Level Set Approach

The development of a digital material framework is presented, allowing to build virtual microstructures in agreement with experimental data. The construction of the virtual material consists in building a multi-level Voronoï tessellation. A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way. A corresponding finite element mesh can be generated automatically in 3D, and used for the simulation of mechanical testing under large strain. In the examples shown in this work, the initial mesh was non uniform and anisotropic, taking into account the presence of interfaces between grains and sub-grains. Automatic remeshing was performed due to the large strains, and maintained the non uniform and anisotropic character of the mesh. A level set approach was used to follow the grain boundaries during the deformation. The grain constitutive law was either a viscoplastic power law, or a crystallographic formulation based on crystal plasticity. Stored energies and precise grain boundary network geometries were obtained directly from the deformed digital sample. This information was used for subsequent modelling of grain growth with the level set approach, on the same mesh.

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