An efficient computational model for water wave propagation in coastal regions

Oliveira, Filipa; Anastasiou, K.

doi:10.1016/s0141-1187(98)00024-8

Cited by 30 publications

(16 citation statements)

References 22 publications

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“…(2) and (18). Figure 6 is a sketch of the two-dimensional flow field and boundary conditions for steady recharge and flow through a two-layered aquifer with a horizontal, impervious bottom and finite, constant head lateral boundaries.…”

Section: Resultsmentioning

confidence: 99%

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Memory allocation and computations for Laplace’s equation of 3-D arbitrary boundary problems

Tsay

2017

MATEC Web Conf.

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Abstract.Computation iteration schemes and memory allocation technique for finite difference method were presented in this paper. The transformed form of a groundwater flow problem in the generalized curvilinear coordinates was taken to be the illustrating example and a 3-dimensional second order accurate 19-point scheme was presented. Traditional element-byelement methods (e.g. SOR) are preferred since it is simple and memory efficient but time consuming in computation. For efficient memory allocation, an index method was presented to store the sparse non-symmetric matrix of the problem. For computations, conjugate-gradientlike methods were reported to be computationally efficient. Among them, using incomplete Choleski decomposition as preconditioner was reported to be good method for iteration convergence. In general, the developed index method in this paper has the following advantages: (1) adaptable to various governing and boundary conditions, (2) flexible for higher order approximation, (3) independence of problem dimension, (4) efficient for complex problems when global matrix is not symmetric, (5) convenience for general sparse matrices, (6) computationally efficient in the most time consuming procedure of matrix multiplication, and (7) applicable to any developed matrix solver.

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Section: Resultsmentioning

confidence: 99%

“…This matrix is useful because M -1 A is closer to an identity matrix than A (Strikwerda, 1989). Algorithms for conjugate-gradient-like methods can be found in many places [5,17,18].…”

Section: The Conjugate-gradient-like Methodsmentioning

confidence: 99%

Memory allocation and computations for Laplace’s equation of 3-D arbitrary boundary problems

Tsay

2017

MATEC Web Conf.

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“…The above criterion is chosen because it is known to be very reliable and also in order to be consistent with other authors like Panchang et al (1991), Li (1994), and Oliveira and Anastasiou (1998).…”

Section: Convergence Criterionmentioning

confidence: 95%

“…Zhao and Anastasiou (1996) used its GMRES method solution to it. Oliveira and Anastasiou (1998) and Zheng et al (2000) used BiCGSTAB method solving it, respectively. All these methods above conform well to the experimental data and can give a quite accurate solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

An efficient and flexible computational model for solving the mild slope equation

Tang

Shen

Zheng

et al. 2004

Coastal Engineering

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“…(3) An iterative approach for solving the elliptic equation, which normally does not require a large amount of computer memory and has a rapid convergence rate, but can be unstable and involves complicated computer algorithms making program maintenance difficult (e.g. Oliveira and Anastasiou, 1998). (4) Direct matrix equation solvers, which are sufficiently robust to handle very complex configurations (e.g.…”

Section: Introductionmentioning

confidence: 99%