scholarly journals An improved fast local level set method for three-dimensional inverse gravimetry

2015 ◽  
Vol 9 (2) ◽  
pp. 479-509 ◽  
Author(s):  
Wangtao Lu ◽  
◽  
Shingyu Leung ◽  
Jianliang Qian ◽  
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Three Dimensional ◽  
Inverse Gravimetry ◽  
Local Level Set

Element-local level set method for three-dimensional dynamic crack growth

2009 ◽  
Vol 80 (12) ◽  
pp. 1520-1543 ◽  
Author(s):  
Qinglin Duan ◽  
Jeong-Hoon Song ◽  
Thomas Menouillard ◽  
Ted Belytschko
Keyword(s):  
Crack Growth ◽  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Three Dimensional ◽  
Dynamic Crack ◽  
Dynamic Crack Growth ◽  
Local Level Set

A Fast Local Level Set Method for Inverse Gravimetry

2011 ◽  
Author(s):  
Victor Isakov ◽  
Shingyu Leung ◽  
Jianliang Qian
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Inverse Gravimetry ◽  
Local Level Set

A Fast Local Level Set Method for Inverse Gravimetry

2011 ◽  
Vol 10 (4) ◽  
pp. 1044-1070 ◽  
Author(s):  
Victor Isakov ◽  
Shingyu Leung ◽  
Jianliang Qian
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Uniqueness Result ◽  
Numerical Continuation ◽  
Unknown Boundary ◽  
Open Set ◽  
Level Set Function ◽  
Inverse Gravimetry ◽  
Local Level Set

AbstractWe propose a fast local level set method for the inverse problem of gravimetry. The theoretical foundation for our approach is based on the following uniqueness result: if an open set D is star-shaped or x3-convex with respect to its center of gravity, then its exterior potential uniquely determines the open set D. To achieve this purpose constructively, the first challenge is how to parametrize this open set D as its boundary may have a variety of possible shapes. To describe those different shapes we propose to use a level-set function to parametrize the unknown boundary of this open set. The second challenge is how to deal with the issue of partial data as gravimetric measurements are only made on a part of a given reference domain Ω. To overcome this difficulty we propose a linear numerical continuation approach based on the single layer representation to find potentials on the boundary of some artificial domain containing the unknown set D. The third challenge is how to speed up the level set inversion process. Based on some features of the underlying inverse gravimetry problem such as the potential density being constant inside the unknown domain, we propose a novel numerical approach which is able to take advantage of these features so that the computational speed is accelerated by an order of magnitude. We carry out numerical experiments for both two- and three-dimensional cases to demonstrate the effectiveness of the new algorithm.

scholarly journals Efficient Local Level Set Method without Reinitialization and Its Appliance to Topology Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Wenhui Zhang ◽  
Yaoting Zhang
Keyword(s):  
Topology Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Computational Efficiency ◽  
Numerical Stability ◽  
Local Level ◽  
Band Model ◽  
Numerical Process ◽  
Local Level Set ◽  
Narrow Band Model

The local level set method (LLSM) is higher than the LSMs with global models in computational efficiency, because of the use of narrow-band model. The computational efficiency of the LLSM can be further increased by avoiding the reinitialization procedure by introducing a distance regularized equation (DRE). The numerical stability of the DRE can be ensured by a proposed conditionally stable difference scheme under reverse diffusion constraints. Nevertheless, the proposed method possesses no mechanism to nucleate new holes in the material domain for two-dimensional structures, so that a bidirectional evolutionary algorithm based on discrete level set functions is combined with the LLSM to replace the numerical process of hole nucleation. Numerical examples are given to show high computational efficiency and numerical stability of this algorithm for topology optimization.

A local level-set method for 3D inversion of gravity-gradient data

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. G35-G51 ◽  
Author(s):  
Wangtao Lu ◽  
Jianliang Qian
Keyword(s):  
Inverse Problem ◽  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Density Contrast ◽  
Gravity Gradient ◽  
Gravity Center ◽  
Level Set Function ◽  
Local Level Set ◽  
Set Function

We have developed a local level-set method for inverting 3D gravity-gradient data. To alleviate the inherent nonuniqueness of the inverse gradiometry problem, we assumed that a homogeneous density contrast distribution with the value of the density contrast specified a priori was supported on an unknown bounded domain [Formula: see text] so that we may convert the original inverse problem into a domain inverse problem. Because the unknown domain [Formula: see text] may take a variety of shapes, we parametrized the domain [Formula: see text] by a level-set function implicitly so that the domain inverse problem was reduced to a nonlinear optimization problem for the level-set function. Because the convergence of the level-set algorithm relied heavily on initializing the level-set function to enclose the gravity center of a source body, we applied a weighted [Formula: see text]-regularization method to locate such a gravity center so that the level-set function can be properly initialized. To rapidly compute the gradient of the nonlinear functional arising in the level-set formulation, we made use of the fact that the Laplacian kernel in the gravity force relation decayed rapidly off the diagonal so that matrix-vector multiplications for evaluating the gradient can be accelerated significantly. We conducted extensive numerical experiments to test the performance and effectiveness of the new method.

Ultrasound image segmentation based on a multi-parameter Gabor filter and multiscale local level set method

2020 ◽  
Vol 13 (5) ◽  
pp. 1075-1084
Author(s):  
CHEN Xiao-dong ◽  
◽  
SHENG Jing ◽  
YANG Jin ◽  
CAI Huai-yu ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Level Set Method ◽  
Level Set ◽  
Gabor Filter ◽  
Local Level ◽  
Ultrasound Image ◽  
Ultrasound Image Segmentation ◽  
Local Level Set

scholarly journals A PDE-Based Fast Local Level Set Method

1999 ◽  
Vol 155 (2) ◽  
pp. 410-438 ◽  
Author(s):  
Danping Peng ◽  
Barry Merriman ◽  
Stanley Osher ◽  
Hongkai Zhao ◽  
Myungjoo Kang
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Local Level ◽  
Local Level Set
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