Finite-difference time-domain method for modelling of seismic wave propagation in viscoelastic media

Kalyani, V. K.; Pallavika,; Chakraborty, Subhankari Prasad

doi:10.1016/j.amc.2014.03.029

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…In fact, all prevalent techniques for spatial discretization can be applied to the viscoelastic equation. See, for example, [9,45] for finite element methods, [3,17,25,38] for mixed finite element methods, [20,54] for finite difference methods, [22,23] for generalized finite difference methods (also known as finite volume element methods), [43] for discontinuous Galerkin methods and [49] for weak Galerkin finite element methods. Recently, the meshless methods also attract much attention in solving the viscoelastic equation (1.1), see for instance [35,37].…”

Section: Introductionmentioning

confidence: 99%

A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation

Fu Li,

Yingxiang Xu

2024

EAJAM

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In this paper, we extend a diagonalization-based parallel-in-time (PinT) algorithm to the viscoelastic equation. The central difference method is used for spatial discretization, while for temporal discretization, we use the Crank-Nicolson scheme. Then an all-at-once system collecting all the solutions at each time level is formed and solved using a fixed point iteration preconditioned by an α-circulant matrix in parallel. Via a rigorous analysis, we find that the spectral radius of the iteration matrix is uniformly bounded by α/(1 − α), independent of the model parameters (the damping coefficient ǫ and the wave velocity γ) and the discretization parameters (the time step τ and the spatial mesh size h). Unlike the classical wave equation with Dirichlet boundary condition where the upper bound α/(1 − α) is very sharp, we find that the occurrence of the damping term −ǫ∆ y t , as well as the large final time T , leads to even faster convergence of the algorithm, especially when α is not very small. We illustrate our theoretical findings with several numerical examples.

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Section: Introductionmentioning

confidence: 99%

A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation

Fu Li,

Yingxiang Xu

2024

EAJAM

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“…One is related to spatial discretized algorithm such as FEM [2] and [3], EFG [4] and [5], BEM [6], etc, and another is associated with the descritized algorithm in the time domain, such as various kinds of FDM [7] and [8].…”

Section: Introductionmentioning

confidence: 99%

A piecewise partitioning Scaled Boundary Finite Element algorithm to solve viscoelastic problems with cyclic symmetry

Wang

Yang

2016

Engineering Analysis with Boundary Elements

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Scaled Boundary Finite Element Method (SBFEM) and a temporally adaptive algorithm are combined to solve viscoelastic problems. By expanding variables at a discretized time interval, a spatially and temporally coupled viscoelastic problem is decoupled into a series of recursive spatial problems, which are solved by SBFEM, the computing accuracy in the time domain is controlled via a self-adaptive process. For the cyclic symmetric structures, the cyclic symmetry is exploited to reduce the computational expense of SBFEM, both the eigenvalue and system equations of SBFEM are partitioned into a number of smaller independent problems, which are solved by a partitioning algorithm. Two numerical examples are given to verify and illustrate the proposed approach.

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Solving viscoelastic problems with cyclic symmetry via a temporally adaptive EFG-SB partitioning algorithm

Guo

Yang

2018

Engineering with Computers

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Finite-difference time-domain method for modelling of seismic wave propagation in viscoelastic media

Cited by 5 publications

References 25 publications

A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation

A Diagonalization-Based Parallel-in-Time Algorithm for Crank-Nicolson’s Discretization of the Viscoelastic Equation

A piecewise partitioning Scaled Boundary Finite Element algorithm to solve viscoelastic problems with cyclic symmetry

Solving viscoelastic problems with cyclic symmetry via a temporally adaptive EFG-SB partitioning algorithm

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