Results 1  10
of
313,622
Fronts propagating with curvature dependent speed: algorithms based on Hamilton–Jacobi formulations
, 1988
"... We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvaturedependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, w ..."
Abstract

Cited by 1167 (60 self)
 Add to MetaCart
, which resemble HamiltonJacobi equations with parabolic righthand sides, by using techniques from hyperbolic conservation laws. Nonoscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps
Solutions of the HamiltonJacobi Equation ∗
, 1999
"... We discuss a new relation between the low lying Schroedinger wave function of a particle in a onedimentional potential V and the solution of the corresponding HamiltonJacobi equation with −V as its potential. The function V is ≥ 0, and can have several minina (V = 0). We assume the problem to be c ..."
Abstract
 Add to MetaCart
We discuss a new relation between the low lying Schroedinger wave function of a particle in a onedimentional potential V and the solution of the corresponding HamiltonJacobi equation with −V as its potential. The function V is ≥ 0, and can have several minina (V = 0). We assume the problem
Hypercontractivity Of HamiltonJacobi Equations
 J. Math. Pures Appl
, 2000
"... .  Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of HamiltonJacobi equations. By the infimumconvolution description of the Hamilt ..."
Abstract

Cited by 124 (19 self)
 Add to MetaCart
.  Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of HamiltonJacobi equations. By the infimumconvolution description
Weighted ENO Schemes for HamiltonJacobi Equations
 SIAM J. Sci. Comput
, 1997
"... In this paper, we present a weighted ENO (essentially nonoscillatory) scheme to approximate the viscosity solution of the HamiltonJacobi equation: OE t +H(x 1 ; \Delta \Delta \Delta ; x d ; t; OE; OE x1 ; \Delta \Delta \Delta ; OE xd ) = 0: This weighted ENO scheme is constructed upon and has the ..."
Abstract

Cited by 225 (0 self)
 Add to MetaCart
In this paper, we present a weighted ENO (essentially nonoscillatory) scheme to approximate the viscosity solution of the HamiltonJacobi equation: OE t +H(x 1 ; \Delta \Delta \Delta ; x d ; t; OE; OE x1 ; \Delta \Delta \Delta ; OE xd ) = 0: This weighted ENO scheme is constructed upon and has
HamiltonJacobi Skeletons
, 1999
"... The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate, ..."
Abstract

Cited by 157 (11 self)
 Add to MetaCart
The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shapefromshading and for recent dynamic theories of shape. Its numerical simulation can be delicate
HamiltonJacobi equation for integrable systems using
"... An approximation method for the stabilizing solution of the ..."
HamiltonJacobi Equations, Conservation Laws and Numerical Algorithms
"... In many physical problems, interfaces move with a speed that depends on the local curvature. Some common examples are flame propagation, crystal growth, and oilwater boundaries. We model the front as a closed, nonintersecting, initial hypersurface flowing along its gradient field with a speed that ..."
Abstract
 Add to MetaCart
of the solution, rather than the global structure. Conversely, the global properties of the motion can be captured by imbedding the surface in a higherdimensional function. In this setting, the equations of motion can be solved using numerical techniques borrowed from hyperbolic conservation laws. We use
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
Abstract

Cited by 616 (22 self)
 Add to MetaCart
describe a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for HamiltonJacobi equations and fast adaptive narrow band level set methods
Results 1  10
of
313,622