# Some new results in multiphase geometrical optics

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 6, page 1203-1231
- ISSN: 0764-583X

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topRunborg, Olof. "Some new results in multiphase geometrical optics." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1203-1231. <http://eudml.org/doc/197596>.

@article{Runborg2010,

abstract = {
In order to accommodate solutions with multiple
phases, corresponding to crossing rays, we
formulate geometrical optics for the scalar wave equation as
a kinetic transport equation set in phase space.
If the maximum number of phases is finite and known a priori we
can recover the exact multiphase solution from an
associated system of moment equations, closed by an assumption
on the form of the density function in the kinetic equation.
We consider two different closure assumptions based on
delta and Heaviside functions and analyze the resulting
equations. They form systems of nonlinear conservation laws
with source terms. In contrast to the classical
eikonal equation, these
equations will incorporate a "finite" superposition principle
in the sense that while the maximum number of phases
is not exceeded a sum of solutions is also a solution.
We present numerical results for a variety
of homogeneous and inhomogeneous problems.
},

author = {Runborg, Olof},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Geometrical optics; multivalued traveltimes; eikonal equation;
kinetic equations; conservation laws; moment equations;
finite difference methods; nonstrictly hyperbolic system.; multivalued travel times; finite difference methods; nonstrictly hyperbolic system; geometrical optics; scalar wave equation; kinetic transport equation; phase space; multiphase solution; nonlinear conservation laws},

language = {eng},

month = {3},

number = {6},

pages = {1203-1231},

publisher = {EDP Sciences},

title = {Some new results in multiphase geometrical optics},

url = {http://eudml.org/doc/197596},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Runborg, Olof

TI - Some new results in multiphase geometrical optics

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 6

SP - 1203

EP - 1231

AB -
In order to accommodate solutions with multiple
phases, corresponding to crossing rays, we
formulate geometrical optics for the scalar wave equation as
a kinetic transport equation set in phase space.
If the maximum number of phases is finite and known a priori we
can recover the exact multiphase solution from an
associated system of moment equations, closed by an assumption
on the form of the density function in the kinetic equation.
We consider two different closure assumptions based on
delta and Heaviside functions and analyze the resulting
equations. They form systems of nonlinear conservation laws
with source terms. In contrast to the classical
eikonal equation, these
equations will incorporate a "finite" superposition principle
in the sense that while the maximum number of phases
is not exceeded a sum of solutions is also a solution.
We present numerical results for a variety
of homogeneous and inhomogeneous problems.

LA - eng

KW - Geometrical optics; multivalued traveltimes; eikonal equation;
kinetic equations; conservation laws; moment equations;
finite difference methods; nonstrictly hyperbolic system.; multivalued travel times; finite difference methods; nonstrictly hyperbolic system; geometrical optics; scalar wave equation; kinetic transport equation; phase space; multiphase solution; nonlinear conservation laws

UR - http://eudml.org/doc/197596

ER -

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