Fabio I. Zyserman

Parallel finite element algorithm with domain decomposition for three-dimensional magnetotelluric modelling

We present a new finite element (FE) method for magnetotelluric modelling of three-dimensional conductivity structures. Maxwells equations are treated as a system of first-order partial differential equations for the secondary fields. Absorbing boundary conditions are introduced, minimizing undesired boundary effects and allowing the use of small computational domains. The numerical algorithm presented here is an iterative, domain decomposition procedure employing a nonconforming FE space. It does not use global matrices, therefore allowing the modellization of large and complicated structures. The algorithm is naturally parallellizable, and we show results obtained in the IBM SP2 parallel supercomputer at Purdue University. The accuracy of the numerical method is verified by checking the computed solutions with the results of COMMEMI, the international project on the comparison of modelling methods for electromagnetic induction.

Brane worlds, string cosmology, and AdS / CFT

Using the thin-shell formalism we discuss the motion of domain walls in de Sitter and anti--de Sitter (AdS) time-dependent bulks. This motion results in a dynamics for the brane scale factor. We show that in the case of a clean brane the scale factor describes both singular and nonsingular universes, with phases of contraction and expansion. These phases can be understood as quotients of AdS spacetime by a discrete symmetry group. We discuss this effect in some detail, and suggest how the AdS/CFT correspondence could be applied to obtain a nonperturbative description of brane-world string cosmology.

Numerical electroseismic modeling: A finite element approach

Abstract Electroseismics is a procedure that uses the conversion of electromagnetic to seismic waves in a fluid-saturated porous rock due to the electrokinetic phenomenon. This work presents a collection of continuous and discrete time finite element procedures for electroseismic modeling in poroelastic fluid-saturated media. The model involves the simultaneous solution of Biot’s equations of motion and Maxwell’s equations in a bounded domain, coupled via an electrokinetic coefficient, with appropriate initial conditions and employing absorbing boundary conditions at the artificial boundaries. The 3D case is formulated and analyzed in detail including results on the existence and uniqueness of the solution of the initial boundary value problem. Apriori error estimates for a continuous-time finite element procedure based on parallelepiped elements are derived, with Maxwell’s equations discretized in space using the lowest order mixed finite element spaces of Nedelec, while for Biot’s equations a nonconforming element for each component of the solid displacement vector and the vector part of the Raviart–Thomas–Nedelec of zero order for the fluid displacement vector are employed. A fully implicit discrete-time finite element method is also defined and its stability is demonstrated. The results are also extended to the case of tetrahedral elements. The 2D cases of compressional and vertically polarized shear waves coupled with the transverse magnetic polarization (PSVTM-mode) and horizontally polarized shear waves coupled with the transverse electric polarization (SHTE-mode) are also formulated and the corresponding finite element spaces are defined. The 1D SHTE initial boundary value problem is also formulated and approximately solved using a discrete-time finite element procedure, which was implemented to obtain the numerical examples presented.

NONCONFORMING FINITE ELEMENT METHODS FOR THE THREE-DIMENSIONAL HELMHOLTZ EQUATION: ITERATIVE DOMAIN DECOMPOSITION OR GLOBAL SOLUTION?

Iterative domain decomposition (DD) nonconforming finite element methods for the Helmholtz equation attempt to solve two problems. First, there exists no efficient algorithms able to solve the large sparse linear system arising from the discretization of the equation via the standard finite elements method. Secondly, even when DD methods generally yield small matrices, standard conforming elements, such as Q1 elements, force the transmission of a relatively large amount of data among subdomains. In this paper, we compared performance of global methods and a set of DD techniques to solve the Helmholtz equation in a three-dimensional domain. The efficiency of the algorithms is measured in terms of CPU time usage and memory requirements. The role of domain size and the linear solver type used to solve each local problem within each subdomain was also analyzed. The numerical results show that iterative DD methods perform far better than global methods. In addition, iterative DD methods involving small subdomains work better than those with subdomains involving a large number of elements. Properties of the iterative DD algorithms such as scalability, robustness, and parallel performance are also analyzed.

GRAVITATIONAL MEMORY OF NATURAL WORMHOLES

A traversable wormhole solution of general scalar–tensor field equations is presented. We have shown, after a numerical analysis for the behavior of the scalar field of Brans–Dicke theory, that the solution is completely singularity-free. Furthermore, the analysis of more general scalar field dependent coupling constants indicates that the gravitational memory phenomenon may play an important role for the fate of natural wormholes.

SH Seismoelectric Response of a Glacier: An Analytic Study

In this work we derive the analytic solutions to the system of equations modeling, within the framework of Pride’s theory, the seismic-to-electromagnetic conversions taking place in a glacial environment. Considering a one dimensional approach, we set a pure shear horizontal (SH) wave seismic source on top of an elastic medium representing the glacier, which overlies a porous medium fully-saturated with water, representing the glacier bed. The obtained solutions allow to separately represent and analyze the induced electromagnetic responses, the so called coseismic waves, for both the electric and magnetic fields along with the signals originated at the glacier bottom, the electric interface response and magnetic interface response. We also propose approximate solutions, useful to be used in a fast inversion algorithm. We analyze the characteristics of the induced electromagnetic signals and their dependence on the type of glacier bed, considering an unconsolidated one and a consolidated one. The main results of the present paper are manifold, on the one hand, the mentioned analytic solutions, on the other hand, that the electric interface response originated at the glacier bottom is proportional to the electric current density at this depth, and depends on textural and †Paseo del Bosque s/n, B1900FWA La Plata, Argentina. ‡5 rue René Descartes, 67084 Strasbourg, France. c ©2018 American Geophysical Union. All Rights Reserved. electrical properties of the basement. We also showed that the amplitude of the electric interface response is three orders of magnitude higher than the amplitude of the electric coseismic field. This fact reinforces the idea proposed in our previous works that it would be interesting to test SH seismoelectrics as a possible geophysical prospecting and monitoring tool. Keypoints: • We derive both exact and approximate analytic solutions to model the SH seismoelectric response of a glacier system • The obtained results suggest that SH seismoelectrics could constitute a possible geophysical prospecting tool c ©2018 American Geophysical Union. All Rights Reserved.