Wavelet preconditioning for the three fields formulation: Numerical results in conforming decomposition

Golbabaee, A.; Mokhtarzadeh, M. R.; Chegini, Nabi; Mokhtary, R.

doi:10.1016/j.amc.2005.04.093

Cited by 2 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This feature of wavelet bases has also been used to solve optimal control problems (Razzaghi and Yousefi, 2002), eigenvalue problems (Mollet et al , 2013) and ordinary differential equations (Homei et al , 2014) adaptively. On the other hand, one can do preconditioning of systems by means of hierarchical structure of wavelets (Golbabaee et al , 2006).…”

Section: Introductionmentioning

confidence: 99%

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

Minbashian

Adibi

Dehghan

2018

HFF

View full text Add to dashboard Cite

Purpose This paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing. Design/methodology/approach The authors use a space-time weak formulation of SWEs which exploits continuous Galerkin (cG) in space and discontinuous Galerkin (dG) in time allowing time stepping, also known as cGdG. Such formulations along with SC term have recently been proved to ensure the stability of fully discrete schemes without scarifying the accuracy. However, the resulting scheme is expensive in terms of number of degrees of freedom (DoFs). By using natural adaptivity of wavelet expansions, the authors devise an adaptive algorithm to reduce the number of DoFs. Findings The proposed algorithm uses DoFs in a dynamic way to capture the shocks in all time steps while keeping the representation of approximate solution sparse. The performance of the proposed scheme is shown through some numerical examples. Originality/value An incorporation of wavelets for adaptivity in space-time weak formulations applied for SWEs is proposed.

show abstract

Section: Introductionmentioning

confidence: 99%

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

Minbashian

Adibi

Dehghan

2018

HFF

View full text Add to dashboard Cite

show abstract

“…By modifying the biorthogonal MRA for L 2 (0, 2) [1,6], we will introduce a MRA for L 2 (0, 2)which is suitable in nonconforming domain decomposition. In numerical implementation, by using the extension operator on the cross points of skeleton and special inverse fast wavelet transforms (IFWTs), we can construct the biorthogonal MRA on the skeleton.…”

Section: Introductionmentioning

confidence: 99%

Application of biorthogonal wavelets to preconditioning the 3-fields formulation: Numerical results in nonconforming decomposition

Chegini¹,

Golbabaee²,

Mokhtari³

2006

imf

Self Cite

View full text Add to dashboard Cite

The aim of this paper is to implement the wavelet preconditioner for the linear system corresponding to the discrete Poincaré-Steklov operator arising in the three fields formulation. In order to apply the preconditioner, we will introduce multiresolution analysis(MRA)for L 2 (0, 2) which is suitable in nonconforming domain decomposition. Extensive numerical results show that the condition number of the matrix after preconditioning is stabilized when the number of subdomains and elements per edge are large.Mathematics Subject Classification: 65N55, 65T60, 35J25.

show abstract

Wavelet preconditioning for the three fields formulation: Numerical results in conforming decomposition

Cited by 2 publications

References 12 publications

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

An adaptive space-time shock capturing method with high order wavelet bases for the system of shallow water equations

Application of biorthogonal wavelets to preconditioning the 3-fields formulation: Numerical results in nonconforming decomposition

Contact Info

Product

Resources

About