Scalar Auxiliary Variable (SAV) Stabilization of Implicit‐Explicit (IMEX) Time Integration Schemes for Non‐Linear Structural Dynamics
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DOI: 10.1002/nme.7660
Abstract: Implicit‐explicit (IMEX) time integration schemes are well suited for non‐linear structural dynamics because of their low computational cost and high accuracy. However, the stability of IMEX schemes cannot be guaranteed for general non‐linear problems. In… read more here.
Keywords: non linear; sav; time integration; imex time ... See more keywords
Randomised one-step time integration methods for deterministic operator differential equations
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DOI: 10.1007/s10092-022-00457-6
Abstract: Uncertainty quantification plays an important role in problems that involve inferring a parameter of an initial value problem from observations of the solution. Conrad et al. (Stat Comput 27(4):1065–1082, 2017 ) proposed randomisation of deterministic… read more here.
Keywords: time; integration methods; time integration; operator differential ... See more keywords
An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics
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DOI: 10.1007/s10483-017-2207-8
Abstract: A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom (SDOF) system, and… read more here.
Keywords: time integration; proposed method; uniform cubic; improved time ... See more keywords
A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions
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DOI: 10.1007/s10915-021-01454-7
Abstract: Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical… read more here.
Keywords: time integration; summation parts; class stable; integration ... See more keywords
Local coordinates on Lie groups for half-explicit time integration of Cosserat-rod models with constraints
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DOI: 10.1007/s11044-024-10002-8
Abstract: Explicit Runge–Kutta methods are the gold standard of time-integration methods for nonstiff problems in system dynamics since they combine a small numerical effort per time step with high accuracy, error control, and straightforward implementation. For… read more here.
Keywords: half explicit; local coordinates; time; time integration ... See more keywords
On the optimization of n-sub-step composite time integration methods
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DOI: 10.1007/s11071-020-06020-8
Abstract: A family of n-sub-step composite time integration methods, which employs the trapezoidal rule in the first $$n-1$$ sub-steps and a general formula in the last one, is discussed in this paper. A universal approach to… read more here.
Keywords: step composite; integration methods; sub step; composite time ... See more keywords
Electromagnetic Analysis Using High-Order Numerical Schemes in Space and Time
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DOI: 10.1007/s11831-017-9249-9
Abstract: The current paper establishes different axisymmetric and two-dimensional models for an electrostatic, magnetostatic and electromagnetic induction process. Therein, the Maxwell equations are combined in a monolithic solution strategy. A higher order finite element discretization using… read more here.
Keywords: time; analysis using; order; time integration ... See more keywords
A novel time integration formulation for nonlinear dynamic analysis
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DOI: 10.1016/j.ast.2017.07.032
Abstract: Abstract To solve the linear and nonlinear dynamic equation of motion, a family of explicit higher-order time integration algorithms is presented. The differential transformation method in conjunction with the state–space concept is used. In this… read more here.
Keywords: time integration; integration formulation; novel time; nonlinear dynamic ... See more keywords
On nonconvex meshes for elastodynamics using virtual element methods with explicit time integration
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DOI: 10.1016/j.cma.2019.06.031
Abstract: Abstract While the literature on numerical methods (e.g. finite elements and, to a certain extent, virtual elements) concentrates on convex elements, there is a need to probe beyond this limiting constraint so that the field… read more here.
Keywords: virtual element; explicit time; time integration; element ... See more keywords
An evaluation of the generalized–α time integration scheme for a transient response of nonlinear structures
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DOI: 10.1016/j.engstruct.2019.109992
Abstract: Abstract The recently developed promising generalized– α time integration scheme for nonlinear structures is evaluated and compared with Bathe scheme. The nonlinear benchmarks are developed and implemented in order to assess reliability and numerical efficiency… read more here.
Keywords: scheme; integration scheme; generalized time; nonlinear structures ... See more keywords
Novel explicit time integration schemes for efficient transient analyses of structural problems
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DOI: 10.1016/j.ijmecsci.2020.105429
Abstract: Abstract In this study, four sets of novel and enhanced two-stage explicit time integration schemes are developed based on a unified set of unconventional approximations. For the development of explicit schemes, truncated Taylor’s series expansions… read more here.
Keywords: time integration; explicit time; algorithmic parameters; integration schemes ... See more keywords