scholarly journals A divide-and-conquer algorithm for seismic data approximation by the Laguerre series

2021 ◽  
Vol 2099 (1) ◽  
pp. 012062
Author(s):  
Andrew V Terekhov
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Divide And Conquer ◽  
Data Approximation ◽  
Laguerre Transform ◽  
Divide And Conquer Algorithm ◽  
The One ◽  
Initial Boundary Value

Abstract An algorithm of the Laguerre transform for approximating functions on large intervals is proposed. The idea of the considered approach is that the calculation of improper integrals of rapidly oscillating functions is replaced by a solution of an initial boundary value problem for the one-dimensional transport equation. It allows one to successfully avoid the problems associated with the stable implementation of the Laguerre transform. A divide-and-conquer algorithm based on shift operations made it possible to significantly reduce the computational cost of the proposed method. Numerical experiments have shown that the methods are economical in the number of operations, stable, and have satisfactory accuracy for seismic data approximation.

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

scholarly journals Biological growth in bodies with incoherent interfaces

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170716 ◽  
Author(s):  
Digendranath Swain ◽  
Anurag Gupta
Keyword(s):  
Nutrient Concentration ◽  
Nutrient Balance ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Cutaneous Wounds ◽  
Incoherent Interface ◽  
Elastic Distortion ◽  
Interfacial Growth ◽  
The One ◽  
Initial Boundary Value

A general theory of thermodynamically consistent biomechanical–biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and elastic distortion tensors at the interface. The incoherent interface therefore acts as an additional source of internal stress besides allowing for rich growth kinematics. All the biochemicals in the model are essentially represented in terms of nutrient concentration fields, in the bulk and at the interface. A nutrient balance law is postulated which, combined with mechanical balances and kinetic laws, yields an initial-boundary-value problem coupling the evolution of bulk and interfacial growth, on the one hand, and the evolution of growth and nutrient concentration on the other. The problem is solved, and discussed in detail, for two distinct examples: annual ring formation during tree growth and healing of cutaneous wounds in animals.

scholarly journals On the Numerical Solution of the Initial-Boundary Value Problem with Neumann Condition for the Wave Equation by the Use of the Laguerre Transform and Boundary Elements Method

2016 ◽  
Vol 10 (4) ◽  
pp. 285-290 ◽  
Author(s):  
Svyatoslav Litynskyy ◽  
Yuriy Muzychuk ◽  
Anatoliy Muzychuk
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Neumann Condition ◽  
Laguerre Transform ◽  
Boundary Elements Method ◽  
Initial Boundary Value

Abstract We consider a numerical solution of the initial-boundary value problem for the homogeneous wave equation with the Neumann condition using the retarded double layer potential. For solving an equivalent time-dependent integral equation we combine the Laguerre transform (LT) in the time domain with the boundary elements method. After LT we obtain a sequence of boundary integral equations with the same integral operator and functions in right-hand side which are determined recurrently. An error analysis for the numerical solution in accordance with the parameter of boundary discretization is performed. The proposed approach is demonstrated on the numerical solution of the model problem in unbounded three-dimensional spatial domain.

scholarly journals Micromechanical modeling of sulphate corrosion in concrete: Influence of ettringite forming reaction

2008 ◽  
Vol 35 (1-3) ◽  
pp. 29-52 ◽  
Author(s):  
M. Basista ◽  
W. Weglewski
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Sodium Sulphate ◽  
Micromechanical Modeling ◽  
Hardened Cement ◽  
Ettringite Formation ◽  
Equivalent Inclusion Method ◽  
The Difference ◽  
The One ◽  
Initial Boundary Value

Two micromechanical models are developed to simulate the expansion of cementitious composites exposed to external sulphate attack. The difference between the two models lies in the form of chemical reaction of the ettringite formation (through-solution vs. topochemical). In both models the Fick's second law with reaction term is assumed to govern the transport of the sulphate ions. The Eshelby solution and the equivalent inclusion method are used to determine the eigenstrain of the expanding ettringite crystals in microcracked hardened cement paste. The degradation of transport properties is studied in the effective medium and the percolation regime. An initial-boundary value problem (2D) of expansion of a mortar specimen immersed in a sodium sulphate solution is solved and compared with available test data. The obtained results indicate that the topochemical mechanism is the one capable of producing the experimentally observed amount of expansion.

scholarly journals The Laguerre spectral method as applied to numerical solution of a two−dimensional linear dynamic seismic problem for porous media

2016 ◽  
Vol 6 (1) ◽  
pp. 208-212
Author(s):  
Abdumauvlen Berdyshev ◽  
Kholmatzhon Imomnazarov ◽  
Jian-Gang Tang ◽  
Aleksander Mikhailov
Keyword(s):  
Porous Media ◽  
Numerical Solution ◽  
Equations Of Motion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Two Dimensional ◽  
Multiprocessor Computer ◽  
Hydrodynamic Approximation ◽  
Laguerre Transform ◽  
Initial Boundary Value

AbstractThe initial boundary value problem of the dynamics of fluid saturated porous media, described by three elastic parameters in the reversible hydrodynamic approximation, is numerically solved. A linear two-dimensional problem as dynamic equations of porous media for components of velocities, stresses and pore pressure is considered. The equations of motion are based on conservation laws and are consistent with thermodynamic conditions. In this case, a medium is considered to be ideally isotropic (in the absence of energy dissipation) and twodimensional heterogeneous with respect to space. For a numerical solution of the dynamic problem of poroelasticity we use the Laguerre transform with respect to time and the finite difference technique with respect to spatial coordinates on the staggered grids with fourth order of accuracy. The description of numerical implementation of the algorithm offered is presented, and its characteristics are analyzed. Numerical results of the simulation of seismic wave fields for the test layered models have been obtained on the multiprocessor computer.

scholarly journals Stability with respect to coefficients of solution of difference schemes approximating initial boundary-value problems for semi-linear hyperbolic equations

2020 ◽  
Vol 64 (2) ◽  
pp. 135-143
Author(s):  
P. P. Matus ◽  
S. V. Lemeshevsky
Keyword(s):  
Difference Scheme ◽  
Hyperbolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Differential Problem ◽  
Domain Of Existence ◽  
The Stability ◽  
The One ◽  
Initial Boundary Value

The stability with respect to coefficients of solution of a difference scheme approximating the initial boundary-value problem for the one-dimensional semi-linear hyperbolic equation is studied. The estimates of the solutions of both differential and difference problems are obtained. In the domain of existence of the solution, the estimates for perturbation of the solution of a difference scheme with respect to perturbation of the coefficients of the equation are obtained. These estimates are consistent with the estimates for the differential problem. In all cases, the method of energy inequalities, the Bihari inequality and its mesh analogue are used.

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