The Lax–Friedrichs sweeping method for optimal control problems in continuous and hybrid dynamics

Kao, Chiu Yen; Navasca, Carmeliza; Osher, Stanley

doi:10.1016/j.na.2005.01.061

Cited by 2 publications

(2 citation statements)

References 12 publications

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“…Fast methods for solving this equation include fast marching methods [17,39,41,42,55] and a variation known as fast sweeping methods [20,21,54,63].…”

Section: Fig 23 Fast Sweeping Process For the Eikonal Equation In mentioning

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%

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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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“…Fast methods for solving this equation include fast marching methods [17,39,41,42,55] and a variation known as fast sweeping methods [20,21,54,63].…”

Section: Fig 23 Fast Sweeping Process For the Eikonal Equation In mentioning

confidence: 99%

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.

View full text Add to dashboard Cite

show abstract

A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations

Parkinson

2021

J Sci Comput

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The Lax–Friedrichs sweeping method for optimal control problems in continuous and hybrid dynamics

Cited by 2 publications

References 12 publications

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

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

A Rotating-Grid Upwind Fast Sweeping Scheme for a Class of Hamilton-Jacobi Equations

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