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Transient waves from internal sources in non-stationary media - Numerical implementation

Åberg, Ingegerd LU (1996) In Technical Report LUTEDX/(TEAT-7048)/1-29/(1996) TEAT-7048.
Abstract
In this paper, the focus is on numerical results from calculations of scattered

direct waves, originating from internal sources in non-stationary, dispersive,

stratified media. The mathematical starting point is a general, inhomogeneous,

linear, first order, 2 × 2 system of equations. Particular solutions

are obtained, as integrals of waves from point sources distributed inside the

scattering medium. Resolvent kernels are used to construct time dependent

fundamental wave functions at the location of the point source. Wave propagators,

closely related to the Green functions, at all times advance these

waves into the surrounding medium. Two illustrative examples are... (More)
In this paper, the focus is on numerical results from calculations of scattered

direct waves, originating from internal sources in non-stationary, dispersive,

stratified media. The mathematical starting point is a general, inhomogeneous,

linear, first order, 2 × 2 system of equations. Particular solutions

are obtained, as integrals of waves from point sources distributed inside the

scattering medium. Resolvent kernels are used to construct time dependent

fundamental wave functions at the location of the point source. Wave propagators,

closely related to the Green functions, at all times advance these

waves into the surrounding medium. Two illustrative examples are given.

First waves, propagating from internal sources in a Klein-Gordon slab, are

calculated with the new method. These wave solutions are compared to alternative

solutions, which can be obtained from analytical fundamental waves,

solving the Klein-Gordon equation in an infinite medium. It is shown, how

the Klein-Gordon wave splitting, which transforms the Klein-Gordon equation

into a set of uncoupled first order equations, can be used to adapt the infi-

nite Klein-Gordon solutions to the boundary conditions of the Klein-Gordon

slab. The second example hints at the extensive possibilities offered by the

new method. The current and voltage waves, evoked on the power line after

an imagined strike of lightning, are studied. The non-stationary properties

are modeled by the shunt conductance, which grows exponentially in time,

together with dispersion in the shunt capacitance. (Less)
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author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7048)/1-29/(1996)
volume
TEAT-7048
pages
29 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
d8e60792-910e-4df2-b822-c625b6218bf6 (old id 530358)
date added to LUP
2007-09-06 11:09:31
date last changed
2016-10-11 08:45:54
@misc{d8e60792-910e-4df2-b822-c625b6218bf6,
  abstract     = {In this paper, the focus is on numerical results from calculations of scattered<br/><br>
direct waves, originating from internal sources in non-stationary, dispersive,<br/><br>
stratified media. The mathematical starting point is a general, inhomogeneous,<br/><br>
linear, first order, 2 × 2 system of equations. Particular solutions<br/><br>
are obtained, as integrals of waves from point sources distributed inside the<br/><br>
scattering medium. Resolvent kernels are used to construct time dependent<br/><br>
fundamental wave functions at the location of the point source. Wave propagators,<br/><br>
closely related to the Green functions, at all times advance these<br/><br>
waves into the surrounding medium. Two illustrative examples are given.<br/><br>
First waves, propagating from internal sources in a Klein-Gordon slab, are<br/><br>
calculated with the new method. These wave solutions are compared to alternative<br/><br>
solutions, which can be obtained from analytical fundamental waves,<br/><br>
solving the Klein-Gordon equation in an infinite medium. It is shown, how<br/><br>
the Klein-Gordon wave splitting, which transforms the Klein-Gordon equation<br/><br>
into a set of uncoupled first order equations, can be used to adapt the infi-<br/><br>
nite Klein-Gordon solutions to the boundary conditions of the Klein-Gordon<br/><br>
slab. The second example hints at the extensive possibilities offered by the<br/><br>
new method. The current and voltage waves, evoked on the power line after<br/><br>
an imagined strike of lightning, are studied. The non-stationary properties<br/><br>
are modeled by the shunt conductance, which grows exponentially in time,<br/><br>
together with dispersion in the shunt capacitance.},
  author       = {Åberg, Ingegerd},
  language     = {eng},
  pages        = {29},
  publisher    = {ARRAY(0x9d9fe98)},
  series       = {Technical Report LUTEDX/(TEAT-7048)/1-29/(1996)},
  title        = {Transient waves from internal sources in non-stationary media - Numerical implementation},
  volume       = {TEAT-7048},
  year         = {1996},
}