Explicit time integration scheme with large time steps for first order transient problems using finite increment calculus

Oñate, Eugenio; de-Pouplana, Ignasi; Zárate, Francisco

doi:10.1016/j.cma.2022.115332

Cited by 2 publications

(11 citation statements)

References 38 publications

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“…Details of the computation of the residual terms in Equation (17) are given in Reference 6. The general expression of the EFT11 scheme can be written in terms of a single stabilization parameters as 6 1 Δt…”

Section: First Order Eft11 Schemementioning

confidence: 99%

“…Assuming a stable solution of the type y n+1 i = 𝛾 i y n i , with 𝛾 i being the amplification factor for the ith mode, we can obtain from Equation (6),…”

Section: The Numerical Solution Of the Semidiscrete Parabolic Equatio...mentioning

confidence: 99%

“…The FIC approach for formulating higher order forms of the differential equation in mechanics has been successfully used, in conjunction with standard numerical methods, such as the FEM and meshless procedures, for finding accurate and stable solutions for steady state and transient problems, such as convection-diffusion-radiation, fluid dynamics and quasi-incompressible solids, among others. 6,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] A general FIC-Time form of the semidiscrete parabolic equation can be written as follows…”

Section: Fic Form Of the Semidiscrete Parabolic Equation In Mechanicsmentioning

confidence: 99%

“…The derivation of the new explicit scheme was based on the finite element calculus (FIC) procedure for modeling the transient heat conduction problem. 6 The stability and time step size of the new explicit FIC-based scheme (hereafter termed explicit FIC-Time scheme, or EFT scheme in short) is governed by a time stabilization parameter. The examples of application in one (1D) and two (2D) dimensions presented in Reference 6 showed that considerable gains in the time step size versus the standard FE scheme were obtained with the EFT scheme, while retaining the accuracy of the transient solution.…”

Section: Introductionmentioning

confidence: 99%

“…In Reference 6 the authors presented a first order explicit time integration scheme for parabolic problems that allows larger time steps than the standard forward Euler (FE) scheme. The derivation of the new explicit scheme was based on the finite element calculus (FIC) procedure for modeling the transient heat conduction problem 6 . The stability and time step size of the new explicit FIC‐based scheme (hereafter termed explicit FIC‐Time scheme , or EFT scheme in short) is governed by a time stabilization parameter.…”

Section: Introductionmentioning

confidence: 99%

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Fast explicit time integration schemes for parabolic problems in mechanics

Oñate,

Zárate,

Gimenez

et al. 2024

Numerical Meth Engineering

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We present a family of fast explicit time integration schemes of first, second and third order accuracy for parabolic problems in mechanics solved via standard numerical methods that have considerable higher computational efficiency versus existing explicit methods of the same order. The derivation of the new explicit schemes is inspired on the finite increment calculus (FIC) procedure used for obtaining stabilized numerical schemes in fluid and solid mechanics. The new (so‐called) explicit FIC‐Time (EFT) schemes allow considerable larger time steps than the standard first order forward Euler (FE) scheme and the second and third order Adams–Bashforth schemes. The comparison with Runge–Kutta schemes also favors the FIC‐Time schemes in terms of the limit time step size (for second order schemes) and the total number of matrix‐vector multiplications per time step (for second and third order schemes). The new first order explicit schemes have a faster convergence to steady‐state than the FE scheme. The accuracy and efficiency of the new EFT schemes are verified in examples of application to the transient heat conduction equation using the finite element method.

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Section: First Order Eft11 Schemementioning

confidence: 99%

“…Assuming a stable solution of the type y n+1 i = 𝛾 i y n i , with 𝛾 i being the amplification factor for the ith mode, we can obtain from Equation (6),…”

Section: The Numerical Solution Of the Semidiscrete Parabolic Equatio...mentioning

confidence: 99%