Search results for "Discretization"
showing 10 items of 237 documents
Inferring rheology and geometry of subsurface structures by adjoint-based inversion of principal stress directions
2020
SUMMARY Imaging subsurface structures, such as salt domes, magma reservoirs or subducting plates, is a major challenge in geophysics. Seismic imaging methods are, so far, the most precise methods to open a window into the Earth. However, the methods may not yield the exact depth or size of the imaged feature and may become distorted by phenomena such as seismic anisotropy, fluid flow, or compositional variations. A useful complementary method is therefore to simulate the mechanical behaviour of rocks on large timescales, and compare model predictions with observations. Recent studies have used the (non-linear) Stokes equations and geometries from seismic studies in combination with an adjoi…
A Variational Formulation of the BEM for Elastic-Plastic Analysis
1990
The quasi-static elastic perfectly plastic analysis problem is approached by the boundary element method (BEM). To this purpose, a time semidiscretization is first achieved by finite intervals (Fl) in order to transform, through a variationally consistent procedure, the evolutive problem into a discrete sequence of inelastic holonomic-type “weighted” problems for each of which a mixed boundary/domain min-max principle is established. This principle is then discretized by means of boundary elements (BE) and cell elements (CE), the latter having the only purpose of suitably interpolating the FI weighted yielding laws within the domain. The algebraic governing equations obtained show symmetry …
A Variationally Consistent Time Modelling of Elastic-Plastic Constitutive Equations
1991
A general energy-based time discretization method for evolutive analysis is presented. Most known time integration procedures (mid-point rule, backward difference, etc.) are shown to be particular cases of it. For space continuous systems, a sequence of weighted boundary value problems of deformation-theory plasticity are obtained, each characterizable by a number of variational principles useful for finite element discretization.
Cell-average WENO with progressive order of accuracy close to discontinuities with applications to signal processing
2020
In this paper we translate to the cell-average setting the algorithm for the point-value discretization presented in S. Amat, J. Ruiz, C.-W. Shu, D. F. Y\'a\~nez, A new WENO-2r algorithm with progressive order of accuracy close to discontinuities, submitted to SIAM J. Numer. Anal.. This new strategy tries to improve the results of WENO-($2r-1$) algorithm close to the singularities, resulting in an optimal order of accuracy at these zones. The main idea is to modify the optimal weights so that they have a nonlinear expression that depends on the position of the discontinuities. In this paper we study the application of the new algorithm to signal processing using Harten's multiresolution. Se…
Quantification des hauteurs de neige et des températures de l'air à la surface d'un glacier : du terrain à l'interpolation, confrontation de méthodes
2009
Quantifying snow cover and surface air temperature on a glacier is usually based on point data. The density of point measures is dependent on the local context. Interpolation brings the opportunity to generate a continuous surface. This surface can be used to derive a global measure for the whole glacier. These measures (total snow water equivalent, average thermal state) are integrated in glaciological and hydrological equations. Interpolation also renders the spatial variations of processes and provides information on inaccessible or not-monitored zones. Using the example of an arctic glacier, several interpolation methods were tested and compared. These methods were applied to snow drill…
Mean square rate of convergence for random walk approximation of forward-backward SDEs
2020
AbstractLet (Y,Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk$B^n$from the underlying Brownian motionBby Skorokhod embedding, one can show$L_2$-convergence of the corresponding solutions$(Y^n,Z^n)$to$(Y, Z).$We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in$C^{2,\alpha}$. The proof relies on an approximative representation of$Z^n$and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to t…
Quantitative comparison of mean field mixing laws for conductivity and dielectric constants of porous media
2003
Abstract Exact numerical solution of the electrostatic disordered potential problem is carried out for four fully discretized three-dimensional experimental reconstructions of sedimentary rocks. The measured effective macroscopic dielectric constants and electrical conductivities are compared with parameter-free predictions from several mean field type theories. All these theories give agreeable results for low contrast between the media. Predictions from local porosity theory, however, match for the entire range of contrast.
Elasticity function of a discrete random variable and its properties
2017
ABSTRACTElasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavia (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuou…
Simulation of BSDEs with jumps by Wiener Chaos Expansion
2016
International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
A numerical assessment of the free energy function for fractional-order relaxation
2014
In this paper a novel method based on complex eigenanalysis in the state variables domain is proposed to uncouple the set of rational order fractional differential equations governing the dynamics of multi-degree-of-freedom system. The traditional complex eigenanalysis is appropriately modified to be applicable to the coupled fractional differential equations. This is done by expanding the dimension of the problem and solving the system in the state variable domain. Examples of applications are given pertaining to multi-degree-of-freedom systems under both deterministic and stochastic loads.