New optimized fourth-order compact finite difference schemes for wave propagation phenomena

Venutelli, Maurizio

doi:10.1016/j.apnum.2014.07.005

Cited by 5 publications

(4 citation statements)

References 42 publications

(66 reference statements)

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“…When using combined error as minimization objective function and emphasis on group velocity, the optimization result will be conservative since the resolution decreases as the weight function increases. However, we believe this may be investigate further for other schemes; in fact, in paper of Venutelli [21], he chooses variations of the phase speed with the wave number for compact scheme optimization, which is directly related to the group velocity error.…”

Section: Comparison Of Minimization Objectivementioning

confidence: 99%

Explicit High Accuracy Maximum Resolution Dispersion Relation Preserving Schemes for Computational Aeroacoustics

Wang

Huang

Liu

et al. 2015

Mathematical Problems in Engineering

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A set of explicit finite difference schemes with large stencil was optimized to obtain maximum resolution characteristics for various spatial truncation orders. The effect of integral interval range of the objective function on the optimized schemes’ performance is discussed. An algorithm is developed for the automatic determination of this integral interval. Three types of objective functions in the optimization procedure are compared in detail, which show that Tam’s objective function gets the best resolution in explicit centered finite difference scheme. Actual performances of the proposed optimized schemes are demonstrated by numerical simulation of three CAA benchmark problems. The effective accuracy, strengths, and weakness of these proposed schemes are then discussed. At the end, general conclusion on how to choose optimization objective function and optimization ranges is drawn. The results provide clear understanding of the relative effective accuracy of the various truncation orders, especially the trade-off when using large stencil with a relatively high truncation order.

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Section: Comparison Of Minimization Objectivementioning

confidence: 99%

Explicit High Accuracy Maximum Resolution Dispersion Relation Preserving Schemes for Computational Aeroacoustics

Wang

Huang

Liu

et al. 2015

Mathematical Problems in Engineering

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“…Yu [49] proposed an optimized DRP-combined CFD scheme to solve the advection equation. Based on the least-squares method, Venutelli [50] developed two optimized fourth-order CFD schemes and presented classical applications for 1D and 2D nonlinear shallow water equations.…”

Section: Introductionmentioning

confidence: 99%

A Compact High-Order Finite-Difference Method with Optimized Coefficients for 2D Acoustic Wave Equation

Liang

Huang

et al. 2023

Remote Sensing

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High-precision finite difference (FD) wavefield simulation is one of the key steps for the successful implementation of full-waveform inversion and reverse time migration. Most explicit FD schemes for solving seismic wave equations are not compact, which leads to difficulty and low efficiency in boundary condition treatment. Firstly, we review a family of tridiagonal compact FD (CFD) schemes of various orders and derive the corresponding optimization schemes by minimizing the error between the true and numerical wavenumber. Then, the optimized CFD (OCFD) schemes and a second-order central FD scheme are used to approximate the spatial and temporal derivatives of the 2D acoustic wave equation, respectively. The accuracy curves display that the CFD schemes are superior to the central FD schemes of the same order, and the OCFD schemes outperform the CFD schemes in certain wavenumber ranges. The dispersion analysis and a homogeneous model test indicate that increasing the upper limit of the integral function helps to reduce the spatial error but is not conducive to ensuring temporal accuracy. Furthermore, we examine the accuracy of the OCFD schemes in the wavefield modeling of complex structures using a Marmousi model. The results demonstrate that the OCFD4 schemes are capable of providing a more accurate wavefield than the CFD4 scheme when the upper limit of the integral function is 0.5π and 0.75π.

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“…With the rapid growth of science and industry in the 20th century, the numerical methods that solve differential equations attract much attentions in different new fields. [1][2][3][4][5] Some of the recent methods include differential transform methods, [6][7][8][9] spectral Galerkin methods, [10][11][12] wavelet methods, 9,[13][14][15][16][17][18] collocation methods, [19][20][21][22][23][24] Legendre methods, [25][26][27] and some other numerical methods for ordinary differential equations. [28][29][30][31][32][33][34][35][36] We consider the following model problem:…”

Section: Introductionmentioning

confidence: 99%

A collocation method for differential equations with one‐point Taylor initial conditions

Ghabarpoor

Kajani

Allame

2019

Math Methods in App Sciences

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This paper presents a new multistep collocation method for nth order differential equations. The interval of interest is first divided into N subintervals. By determining interval conditions in Taylor interpolation in each subinterval, Taylor polynomials are calculated with different step lengths. Then the obtained solutions in each subinterval are used as initial conditions in the next step. Optimal error is assessed using Peano lemma, which shows that the errors decay by decreasing the step length. In particular, for fixed step length h, the error is of O(m−m), where m is the number of collocation points in each subinterval. Meanwhile, for fixed m, the error is of O(hm). Numerical examples demonstrate the validity and high accuracy of the proposed method even for stiff problems.

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New optimized fourth-order compact finite difference schemes for wave propagation phenomena

Cited by 5 publications

References 42 publications

Explicit High Accuracy Maximum Resolution Dispersion Relation Preserving Schemes for Computational Aeroacoustics

Explicit High Accuracy Maximum Resolution Dispersion Relation Preserving Schemes for Computational Aeroacoustics

A Compact High-Order Finite-Difference Method with Optimized Coefficients for 2D Acoustic Wave Equation

A collocation method for differential equations with one‐point Taylor initial conditions

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