A time‐staggered partitioned coupling algorithm for transient heat conduction

Nakshatrala, P. B.; Nakshatrala, K. B.; Tortorelli, Daniel A.

doi:10.1002/nme.2524

Cited by 27 publications

(9 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The use of different time-steps in different subdomains is referred to as multi-time-stepping or subcycling. Some representative works in this direction are [12][13][14]. But many of the prior efforts on mixed methods and multi-time-stepping suffer from one or more of the following deficiencies: (i) The method cannot handle multiple subdomains.…”

Section: Introductionmentioning

confidence: 99%

On multi-time-step monolithic coupling algorithms for elastodynamics

Karimi

Nakshatrala

2014

Journal of Computational Physics

View full text Add to dashboard Cite

We present a way of constructing multi-time-step monolithic coupling methods for elastodynamics. The governing equations for constrained multiple subdomains are written in dual Schur form and enforce the continuity of velocities at system time levels. The resulting equations will be in the form of differential-algebraic equations. To crystallize the ideas we shall employ Newmark family of time-stepping schemes. The proposed method can handle multiple subdomains, and allows different time-steps as well as different time stepping schemes from the Newmark family in different subdomains. We shall use the energy method to assess the numerical stability, and quantify the influence of perturbations under the proposed coupling method. We also discuss the conditions under which the proposed method will be energy preserving, and the conditions under which the method will be energy conserving. Several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method. We shall also compare the proposed multi-time-step coupling method with some other similar methods available in the literature

show abstract

Section: Introductionmentioning

confidence: 99%

On multi-time-step monolithic coupling algorithms for elastodynamics

Karimi

Nakshatrala

2014

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…A more detailed description of the modelling approaches can be found in [3]. Besides adaptivity techniques in both, the spatial and temporal domain and an in Section 22: Scientific computing time integrated heat source, the computational domain is, based on [4], split into sub-domains Ω i , leading to:…”

Section: Thermal Model and Multi-time-steppingmentioning

confidence: 99%

“…The respective parts in black correspond to the weak form of the thermal problem for the sub-domains (κ, f and q denote the thermal conductivity, a heat source and boundary fluxes), whereas the red parts arise due to the weak imposition of the constraints on the interface Γ, that aim to set the jumps of the temperatures as well as the jumps of the fluxes to zero (l denotes the smallest edge length of the mesh and η a penalty parameter used for the weak imposition). In the present approach the interface terms a treated explicit in time, which decouples the sub-domains and allows for a separate integration in time [4].…”

Section: Thermal Model and Multi-time-steppingmentioning

confidence: 99%

“…In the following example a two-dimensional domain for a selective laser beam melting process of TiAl6V4 is split into two sub-domains and solved with the time step sizes ∆t 1 = ∆t2 10 and the so-called system time step ∆t 2 = ∆t sys = 30 µs. The needed penalty parameter η is set to be 37.75 based on the estimator given in [4]. The path of the beam is depicted in Fig.…”

Section: Numerical Examplementioning

confidence: 99%

See 1 more Smart Citation

Domain decomposition applied to the thermal model of selective beam melting processes

Soldner

Steinmann

Mergheim

2018

Proc Appl Math and Mech

View full text Add to dashboard Cite

ErlangenThe utilization of additive manufacturing enables the realization of rather complex part geometries. In the context of powder bed-based selective beam melting processes, parts are built in a layer-by-layer fashion by locally fusing powdered material using either a laser or electron beam. The simulation of powder bed-based additive manufacturing processes for both, polymers as well as metals, is usually a computationally expensive task. This is especially due to the different involved time and length scales, highly non-linear material behaviour and dynamic growth of the simulation domain. Hence, several numerical methods are ought to be combined in order to reduce the associated computational cost. Therefore we employ adaptivity in the spatial and temporal domain. This allows to have locally refined regions that are currently exposed to the beam, while coarsening the discretization in areas that are currently not exposed to the beam. In addition the path of the heat input is integrated in time, which renders a line heat input model. Furthermore, domain decomposition (Multi-Time-Stepping) is applied to account for the different requirements regarding the temporal discretization of different parts of the considered domain. This renders a time integration scheme with distinct time step sizes for different partitions of the domain.

show abstract

“…The proposed methods were not A‐stable and made use of stabilization techniques that often depended on arbitrary constants. In 14, the authors presented similar algorithms with implicit–explicit coupling, in order to use explicit integrators with fine time steps in stiff mesh regions and implicit integrators with coarse time steps in non‐stiff mesh regions. They employed the generalized‐α method 15 and the classical fourth‐order RK scheme to analyze the implications of different time integrators.…”

Section: Introductionmentioning

confidence: 99%

Novel partitioned time integration methods for DAE systems based on L‐stable linearly implicit algorithms

Cui

Bursi

Bonelli

et al. 2011

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYReal-time applications based on the principle of Dynamic Substructuring require integration methods that can deal with constraints without exceeding an a priori fixed number of steps. For these applications, first we introduce novel partitioned algorithms able to solve DAEs arising from transient structural dynamics. In particular, the spatial domain is partitioned into a set of disconnected subdomains and continuity conditions of acceleration at the interface are modeled using a dual Schur formulation. Interface equations along with subdomain equations lead to a system of DAEs for which both staggered and parallel procedures are developed. Moreover under the framework of projection methods, also a parallel partitioned method is conceived. The proposed partitioned algorithms enable a Rosenbrock-based linearly implicit LSRT2 method, to be strongly coupled with different time steps in each subdomain. Thus, user-defined algorithmic damping and subcycling strategies are allowed. Secondly, the paper presents the convergence analysis of the novel schemes for linear single-Degree-of-Freedom (DoF) systems. The algorithms are generally A-stable and preserve the accuracy order as the original monolithic method. Successively, these results are validated via simulations on single-and three-DoFs systems. Finally, the insight gained from previous analyses is confirmed by means of numerical experiments on a coupled spring-pendulum system.

show abstract

A time‐staggered partitioned coupling algorithm for transient heat conduction

Cited by 27 publications

References 23 publications

On multi-time-step monolithic coupling algorithms for elastodynamics

On multi-time-step monolithic coupling algorithms for elastodynamics

Domain decomposition applied to the thermal model of selective beam melting processes

Novel partitioned time integration methods for DAE systems based on L‐stable linearly implicit algorithms

Contact Info

Product

Resources

About