Invariant imbedding and the numerical determination of Green's functions

1970 ◽  
Vol 6 (6) ◽  
pp. 415-423 ◽  
Author(s):  
R. Huss ◽  
R. Kalaba
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Determination ◽  
Invariant Imbedding

BOUNDARY ELEMENT METHOD FOR ISOTROPIC MEDIA WITH RANDOM SHEAR MODULI

2005 ◽  
Vol 13 (01) ◽  
pp. 229-258 ◽  
Author(s):  
HOLGER WAUBKE
Keyword(s):  
Shear Modulus ◽  
Wave Velocity ◽  
Green's Functions ◽  
Polynomial Chaos ◽  
Green’S Functions ◽  
Nonlinear Problems ◽  
System Matrix ◽  
Large Variability ◽  
Shear Moduli

Green's functions for elastic solids with random properties are usually derived by means of the perturbation method. This paper deals with a new approach that has the potential to deal with a large variability of random shear modulus based on the transformation of a polynomial chaos. The deterministic Green's functions for stresses and displacements and the principal values in the boundary integrals caused by a pressure load on the surface are nonlinear transformations of the random variables. A series of transformations of the polynomial chaos is used to transform significant parts of the equation. The first operation is a projection of the log normal distributed shear modulus to a series of Hermite's polynomials based on a Gaussian variable. The second operation is the determination of an arbitrary potential of the wave velocity. The last operation, similar to the first one, consists in the determination of an exponential function depending on the inverse of the wave velocity. These operations, together with multiplications and summations, transform the complete relation from the random shear modulus to Green's functions and principal values. The inversion of the system matrix is already derived for the random finite element approach. The operations are independent of the specific problem and can be applied to almost all acoustic media and similar nonlinear problems.

Time-Domain Poroelastic Green's Functions

2003 ◽  
Vol 11 (03) ◽  
pp. 491-501 ◽  
Author(s):  
Andrzej Hanyga
Keyword(s):  
Differential Equations ◽  
Asymptotic Solution ◽  
Time Domain ◽  
Green's Functions ◽  
Green’S Functions ◽  
Isotropic Case ◽  
The Time Domain ◽  
Singular Memory ◽  
Asymptotic Time

A method previously developed for asymptotic solution of systems of integro-differential equations with singular memory is applied to the determination of the time-domain asymptotic Green's function of Biot's poroelasticity. Asymptotic time-domain Green's functions are constructed in a neighborhood of the wavefronts. The general anisotropic medium as well as the isotropic case are considered.

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