scholarly journals Calculation of wave propagation into land-fast ice

2001 ◽  
Vol 33 ◽  
pp. 322-326 ◽  
Author(s):  
Hyuck Chung ◽  
Colin Fox
Keyword(s):  
Exact Solution ◽  
Wave Propagation ◽  
Numerical Methods ◽  
Numerical Computation ◽  
Direct Calculation ◽  
Integral Form ◽  
Ocean Waves ◽  
Reflection And Transmission ◽  
Recent Developments ◽  
Fast Ice

AbstractWe review the various numerical methods that have been developed for calculating the reflection and transmission of ocean waves at a land-fast ice boundary, including recent developments. While an integral form of the solution, found by the Wiener-Hopf technique, has been known for many years, direct numerical computation of this exact solution has been thought to be prohibitively difficult. Instead, several numerical "matching" procedures have been developed, including some that are only approximate, along with asymptotic solutions based on the integral form. Recently it has been discovered that direct calculation of the integral form is feasible, actually requiring less computation than the matching methods. We outline the actual computations required and contrast each method, and provide examples of computation from the integral form.

Solution of heat and mass transfer problems with non-linear coefficients

2019 ◽  
Vol 5 (4) ◽  
pp. 10-20
Author(s):  
Boris G. Aksenov ◽  
Yuri E. Karyakin ◽  
Svetlana V. Karyakina
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Numerical Methods ◽  
Heat And Mass Transfer ◽  
Unknown Function ◽  
Comparison Theorems ◽  
Upper And Lower Bounds ◽  
Maximum Deviation ◽  
Approximate Methods ◽  
Nonmonotonic Dependence

Equations, which have nonlinear nonmonotonic dependence of one of the coefficients on an unknown function, can describe processes of heat and mass transfer. As a rule, existing approximate methods do not provide solutions with acceptable accuracy. Numerical methods do not involve obtaining an analytical expression for the unknown function and require studying the convergence of the algorithm used. The value of absolute error is uncertain. The authors propose an approximate method for solving such problems based on Westphal comparison theorems. The comparison theorems allow finding upper and lower bounds of the unknown exact solution. A special procedure developed for the stepwise improvement of these bounds provide solutions with a given accuracy. There are only a few problems for equations with nonlinear nonmonotonic coefficients for which the exact solution has been obtained. One of such problems, presented in this article, shows the efficiency of the proposed method. The results prove that the proposed method for obtaining bounds of the solution of a nonlinear nonmonotonic equation of parabolic type can be considered as a new method of the approximate analytical solution having guaranteed accuracy. In addition, the proposed here method allows calculating the maximum deviation from the unknown exact solution of the results of other approximate and numerical methods.

Chebyshev multidomain pseudospectral method to solve cardiac wave equations with rotational anisotropy

2018 ◽  
Vol 09 (04) ◽  
pp. 1850025 ◽  
Author(s):  
Jairo Rodríguez-Padilla ◽  
Daniel Olmos-Liceaga
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Finite Difference Schemes ◽  
Cardiac Models ◽  
Computational Resources ◽  
Realistic Geometries

The implementation of numerical methods to solve and study equations for cardiac wave propagation in realistic geometries is very costly, in terms of computational resources. The aim of this work is to show the improvement that can be obtained with Chebyshev polynomials-based methods over the classical finite difference schemes to obtain numerical solutions of cardiac models. To this end, we present a Chebyshev multidomain (CMD) Pseudospectral method to solve a simple two variable cardiac models on three-dimensional anisotropic media and we show the usefulness of the method over the traditional finite differences scheme widely used in the literature.

Compressed wavefield extrapolation

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM77-SM93 ◽  
Author(s):  
Tim T. Lin ◽  
Felix J. Herrmann
Keyword(s):  
Wave Propagation ◽  
Compressed Sensing ◽  
Signal Recovery ◽  
New Paradigm ◽  
New Approach ◽  
Measurement Basis ◽  
Recent Developments ◽  
Data Volume ◽  
Extrapolation Problem ◽  
Wavefield Extrapolation

An explicit algorithm for the extrapolation of one-way wavefields is proposed that combines recent developments in information theory and theoretical signal processing with the physics of wave propagation. Because of excessive memory requirements, explicit formulations for wave propagation have proven to be a challenge in 3D. By using ideas from compressed sensing, we are able to formulate the (inverse) wavefield extrapolation problem on small subsets of the data volume, thereby reducing the size of the operators. Compressed sensing entails a new paradigm for signal recovery that provides conditions under which signals can be recovered from incomplete samplings by nonlinear recovery methods that promote sparsity of the to-be-recovered signal. According to this theory, signals can be successfully recovered when the measurement basis is incoherent with the representa-tion in which the wavefield is sparse. In this new approach, the eigenfunctions of the Helmholtz operator are recognized as a basis that is incoherent with curvelets that are known to compress seismic wavefields. By casting the wavefield extrapolation problem in this framework, wavefields can be successfully extrapolated in the modal domain, despite evanescent wave modes. The degree to which the wavefield can be recovered depends on the number of missing (evanescent) wavemodes and on the complexity of the wavefield. A proof of principle for the compressed sensing method is given for inverse wavefield extrapolation in 2D, together with a pathway to 3D during which the multiscale and multiangular properties of curvelets, in relation to the Helmholz operator, are exploited. The results show that our method is stable, has reduced dip limitations, and handles evanescent waves in inverse extrapolation.

scholarly journals Evaluation of Pile’s Buckling Under Axial Load by B-Spline Method and Comparison With Finite Element Method and Exact Solution

2018 ◽  
Vol 8 (2) ◽  
pp. 29-34
Author(s):  
A. Moghaddam ◽  
A. Nayeri ◽  
S.M. Mirhosseini
Keyword(s):  
Finite Element Method ◽  
Exact Solution ◽  
Finite Element ◽  
Numerical Methods ◽  
High Volume ◽  
Spline Method ◽  
B Spline ◽  
Volume Calculations ◽  
Reaction Coefficient ◽  
Element Method

Abstract Although various analytical and numerical methods have been proposed by researchers to solve equations, but use of numerical tools with low volume calculations and high accuracy instead of other numerical methods with high volume calculations is inevitable in the analysis of engineering equations. In this paper, B-Spline spectral method was used to study buckling equations of the piles. Results were compared with the calculated amounts of the exact solution and finite element method. Uniform horizontal reaction coefficient has been used in most of proposed methods for analyzing buckling of the pile on elastic base. In reality, soil horizontal reaction coefficient is nonlinear along the pile. So, in this research by using B-Spline method, buckling equation of the pile with nonlinear horizontal reaction coefficient of the soil was investigated. It is worth mentioning that B-Spline method had not been used for buckling of the pile.

scholarly journals An Euler-Lagrange Equation only Depending on Derivatives of Caputo for Fractional Variational Problems with Classical Derivatives

2020 ◽  
Vol 8 (2) ◽  
pp. 590-601
Author(s):  
Melani Barrios ◽  
Gabriela Reyero
Keyword(s):  
Exact Solution ◽  
Variational Problem ◽  
Lagrange Equation ◽  
Integral Form ◽  
Variational Problems ◽  
The Other ◽  
Isoperimetric Problems ◽  
Caputo Derivatives ◽  
Fractional Variational Problems ◽  
Derivatives Of

In this paper we present advances in fractional variational problems with a Lagrangian depending on Caputofractional and classical derivatives. New formulations of the fractional Euler-Lagrange equation are shown for the basic and isoperimetric problems, one in an integral form, and the other that depends only on the Caputo derivatives. The advantage is that Caputo derivatives are more appropriate for modeling problems than the Riemann-Liouville derivatives and makes the calculations easier to solve because, in some cases, its behavior is similar to the behavior of classical derivatives. Finally, anew exact solution for a particular variational problem is obtained.

scholarly journals Wave Propagation Across Acoustic/Biot’s Media: A Finite-Difference Method

2013 ◽  
Vol 13 (4) ◽  
pp. 985-1012 ◽  
Author(s):  
Guillaume Chiavassa ◽  
Bruno Lombard
Keyword(s):  
Wave Propagation ◽  
Numerical Methods ◽  
Heterogeneous Media ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Compressional Wave ◽  
Interface Conditions ◽  
Immersed Interface Method ◽  
Fluid Medium ◽  
Strang Splitting

AbstractNumerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot’s equations (in the porous medium). Interface conditions are introduced to model various hydraulic contacts between the two media: open pores, sealed pores, and imperfect pores. Well-posedness of the initial-boundary value problem is proven. Cartesian grid numerical methods previously developed in porous heterogeneous media are adapted to the present context: a fourth-order ADER scheme with Strang splitting for time- marching; a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory; and an immersed interface method to discretize the interface conditions and to introduce a subcell resolution. Numerical experiments and comparisons with exact solutions are proposed for the three types of interface conditions, demonstrating the accuracy of the approach.

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