Level-set function approach to an inverse interface problem

Ito, Kazufumi; Kunisch, Karl; Li, Zhilin

doi:10.1088/0266-5611/17/5/301

Cited by 168 publications

(189 citation statements)

References 13 publications

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“…Since the expansion carries precise information on the shape of the inclusion, we will show how it can be efficiently exploited for designing significantly better algorithms. In connection with the reconstruction of interfaces, we refer readers to [6,12,17]. This paper is organized as follows: In section 2 we derive higher-order terms in the asymptotic expansion of a certain boundary integral operator which appears in the representation of the steady-state voltage potential.…”

Section: ν(X) |X − Y| 2 ϕ(Y)dσ(y)mentioning

confidence: 99%

Conductivity interface problems. Part I: Small perturbations of an interface

Ammari

Kang

Lim

et al. 2009

Trans. Amer. Math. Soc.

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Abstract. We derive high-order terms in the asymptotic expansions of boundary perturbations of steady-state voltage potentials resulting from small perturbations of the shape of a conductivity inclusion with C 2 -boundary. Our derivation is rigorous and based on layer potential techniques. The asymptotic expansion in this paper is valid for C 1 -perturbations and inclusions with extreme conductivities. It extends those already derived for small volume conductivity inclusions and leads us to very effective algorithms for determining lower-order Fourier coefficients of the shape perturbation of the inclusion based on boundary measurements. We perform some numerical experiments using the algorithm to test its effectiveness.

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Section: ν(X) |X − Y| 2 ϕ(Y)dσ(y)mentioning

confidence: 99%

Conductivity interface problems. Part I: Small perturbations of an interface

Ammari

Kang

Lim

et al. 2009

Trans. Amer. Math. Soc.

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“…Level-set representations [32] have been applied to a host of interface deformation problems in mathematical applications [30,42], including shape optimization [2,7,11,19,26,31,38,40,58,60]. (See [3,5,8] for related phase-field shape optimization.)…”

Section: Level-set Formmentioning

confidence: 99%

“…The most common type of radiation therapy utilizes a medical linear accelerator to deliver high energy (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) MeV range) radiation. The accelerator is mounted on a gantry to adjust the direction of radiation beams, and with a multileaf collimator (MLC) attached in front, to shape the beams.…”

Section: Introductionmentioning

confidence: 99%

Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Radiotherapy Treatment

Cheng¹,

Dong²,

Men³

et al. 2013

SIAM J. Sci. Comput.

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Abstract. We introduce, in this paper, a variational framework for the construction of improved treatment plans in volumetric modulated arc therapy for cancer treatment. This framework consists of a shape optimization component, from the molding of beam shapes, as well as strong constraints, from the equipment involved, on both beam shapes and intensities. We apply the binary level-set method, to handle complex shape topologies, and the fast sweeping method, to handle beam intensity constraints. The result is a fast, flow-based algorithm, in a simplified setting, that guarantees energy decrease. We include numerical simulations of clinical cases to demonstrate the efficacy of the approach.

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“…In particular, their ability to deal with changes in topology without any remeshing has been recognized [10,11]. They have been used in several fields of geophysics and geomechanics, including modeling of two-phase flows and permeability estimation in reservoir simulations [11,12], tectonic plates subduction [13,14], seismic waves travel time computation [15], and, generally, for inverse problems and optimal design [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Modeling, with a unified level-set representation, of the expansion of a hollow in the ground under different physical phenomena

2009

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This paper builds on the flexibility of the level-set representation to model in a unified manner the expansion of a hollow in the ground under different physical phenomena. In particular, the dissolving action of a flow of water in a saturated soil, and that of a jet of particles of water in a nonsaturated one, are represented in a common framework. In that manner, the complex geometrical evolutions of the hollow can be followed without the need for remeshing and this approach allows for a smooth transition between saturated and non-saturated models of the soil. Implementation and numerical difficulties are discussed and two applications of industrial interest are considered. The first one describes the modeling of the piping phenomenon, and the second one the evolution of an excavation created by a leaking duct.

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Level-set function approach to an inverse interface problem

Cited by 168 publications

References 13 publications

Conductivity interface problems. Part I: Small perturbations of an interface

Conductivity interface problems. Part I: Small perturbations of an interface

Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Radiotherapy Treatment

Modeling, with a unified level-set representation, of the expansion of a hollow in the ground under different physical phenomena

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