2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal,
Electron. J. Diff. Eqns., Conference 22 (2015), pp. 117-137.
Transparent boundary conditions for the wave equation in
one dimension and for a Dirac-like equation
M. Pilar Velasco, David Usero, Salvador Jimenez, Luis Vazquez
Abstract:
We present a method to achieve transparent boundary conditions
for the one-dimensional wave equation, and show its numerical implementation
using a finite-difference method. We also present an alternative method for
building the same transparent boundary conditions using a Dirac-like equation
and a Spinor-like formalism. Finally, we extend our method to the
three-dimensional wave equation with radial symmetry.
Published November 20, 2015.
Math Subject Classifications: 35L05, 65M06.
Key Words: Wave equation; transparent boundary condition; Dirac-type equation.
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M. Pilar Velasco
Área de Matemáticas, Estadística
e Investigación operativa
Centro Universitario de la Defensa
Academia General Militar,
50090 Zaragoza, Spain
email: velascom@unizar.es
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David Usero
Sección Departamental de Matemática Aplicada
Facultad de CC. Químicas
Universidad Complutense de Madrid
28040 Madrid, Spain
email: umdavid@mat.ucm.es
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Salvador Jiménez
Departamento de Matemática Aplicada a las
TT. II., E.T.S.I. Telecomunicación
Universidad Politéecnica de Madrid
28040 Madrid, Spain
email: s.jimenez@upm.es
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Luis Vázquez
Departamento de Matemática Aplicada
Facultad de Informática
Universidad Complutense de Madrid
28040 Madrid, Spain
email: lvazquez@fdi.ucm.es
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