Numerical methods for inverse problems in three-dimensional geophysical modeling

1988 ◽  
Vol 4 (1) ◽  
pp. 97-139 ◽  
Author(s):  
V. Pereyra
Keyword(s):  
Numerical Methods ◽  
Inverse Problems ◽  
Three Dimensional ◽  
Geophysical Modeling

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

A Simple Approach to the Study of Wave Patterns

2014 ◽  
Vol 156 (A3) ◽  
Keyword(s):  
Numerical Methods ◽  
Shallow Water ◽  
Froude Number ◽  
Critical Speed ◽  
Graphical Method ◽  
Three Dimensional ◽  
Simple Approach ◽  
Critical Depth ◽  
Simple Manner ◽  
Wave Patterns

The paper revisits some pioneering work of Sir Thomas Havelock on wave patterns with particular attention focused on his graphical method of analysis. Motivated by a desire to explore this method further using numerical methods, it is extended in a simple manner to give three-dimensional illustrations of the wave patterns of a point disturbance in deep and shallow water. All results are confined to the sub- and trans-critical regimes with some obtained very close to the critical Depth Froude Number. Some conclusions are drawn on the wave types produced when operating close to the critical speed and their decay with distance off.

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.

THREE-DIMENSIONAL LIGHT BULLETS IN CUBIC–QUINTIC MEDIA STABILIZED BY PERIODIC VARIATION OF DIFFRACTION AND DISPERSION

2010 ◽  
Vol 19 (03) ◽  
pp. 459-470 ◽  
Author(s):  
P. A. SUBHA ◽  
K. K. ABDULLAH ◽  
V. C. KURIAKOSE
Keyword(s):  
Numerical Methods ◽  
Variational Analysis ◽  
Schrodinger Equation ◽  
Averaging Method ◽  
Three Dimensional ◽  
Periodic Variation ◽  
Varying Coefficients ◽  
Varying Dispersion ◽  
Light Bullets ◽  
Quintic Nonlinear Schrödinger Equation

We propose a dispersion-managed model with diffraction management for the stabilization of three-dimensional spatiotemporal solitons in bulk cubic–quintic media. The cubic–quintic nonlinear Schrödinger equation with periodically varying dispersion and diffraction has been studied using analytical and numerical methods. Variational analysis and the Kapitsa averaging method have been used to study the system analytically. The study has shown that periodically varying coefficients of diffraction and dispersion stabilizes the spatiotemporal solitons in cubic–quintic media.

scholarly journals Numerical methods for multiscale inverse problems

2017 ◽  
Vol 15 (2) ◽  
pp. 305-328 ◽  
Author(s):  
Christina Frederick ◽  
Björn Engquist
Keyword(s):  
Numerical Methods ◽  
Inverse Problems
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