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Analytical Inversion (analytical + inversion)

Distribution by Scientific Domains

Engineering	75%

Selected Abstracts

Analytical inversion of the Jacobian for a class of generalized standard materials

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Felix Fritzen
In this paper we derive an analytical expression for the inverse of the Jacobian occuring in the implicit time integration procedure for a large class of generalized standard materials. The resulting expression is easy to construct and implement into arbitrary programming languages. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Time domain 3D fundamental solutions for saturated poroelastic media with incompressible constituents

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2008
Mohsen Kamalian
Abstract This paper presents simple time domain fundamental solutions for the three-dimensional (3D) well known u,p formulation of saturated porous media, neglecting the compressibility of fluid and solid particles. At first, the corresponding boundary integral equations as well as the explicit Laplace transform domain fundamental solutions are obtained in terms of solid displacements and fluid pressure. Subsequently, the closed form time domain fundamental solutions are derived by analytical inversion of the Laplace transform domain solutions. Finally, a set of numerical results are presented which demonstrate the accuracies and some salient features of the derived analytical transient fundamental solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Time 2D fundamental solution for saturated porous media with incompressible fluid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 3 2005
Behrouz Gatmiri
Abstract The derivation of analytical transient two-dimensional fundamental solution for porous media saturated with incompressible fluid in u-p formulation is discussed in detail. First, the explicit Laplace transform solution in terms of solid displacements and fluid pressure are obtained. Then, the closed-form time-dependent fundamental solution is derived by the analytical inversion of the Laplace transform solution. Finally, a set of numerical results is presented to investigate the accuracy of the proposed solution. It is shown that this solution can be considered as a good approximation of exact solution, especially for the long time. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Analytical and 3-D numerical modelling of Mt. Etna (Italy) volcano inflation

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2005
A. Bonaccorso
SUMMARY Since 1993, geodetic data obtained by different techniques (GPS, EDM, SAR, levelling) have detected a consistent inflation of the Mt. Etna volcano. The inflation, culminating with the 1998,2001 strong explosive activity from summit craters and recent 2001 and 2002 flank eruptions, is interpreted in terms of magma ascent and refilling of the volcanic plumbing system and reservoirs. We have modelled the 1993,1997 EDM and GPS data by 3-D pressurized sources to infer the position and dimension of the magma reservoir. We have performed analytical inversions of the observed deformation using both spheroidal and ellipsoidal sources embedded in a homogeneous elastic half-space and by applying different inversion methods. Solutions for these types of sources show evidence of a vertically elongated magma reservoir located 6 km beneath the summit craters. The maximum elevation of topography is comparable to such depth and strong heterogeneities are inferred from seismic tomography; in order to assess their importance, further 3-D numerical models, employing source parameters extracted from analytical models, have been developed using the finite-element technique. The deformation predicted by all the models considered shows a general agreement with the 1993,1997 data, suggesting the primary role of a pressure source, while the complexities of the medium play a minor role under elastic conditions. However, major discrepancies between data and models are located in the SE sector, suggesting that sliding along potential detachment surfaces may contribute to amplify deformation during the inflation. For the first time realistic features of Mt. Etna are studied by a 3-D numerical model characterized by the topography and lateral variations of elastic structure, providing a framework for a deeper insight into the relationships between internal sources and tectonic structures. [source]