Truncated Integration for Simultaneous Simulation of Sintering Using a Separated Representation

Abstract

Recent developments of multidimensional solvers using separated representation make it possible to account for the multidimensionality of mechanical models in materials science when doing numerical simulations. This paper aims to extend the separated representation to inseparable equations using an efficient integration scheme. It focuses on the dependence of constitutive equations on material coefficients. Although these coefficients can be optimized using few experimental results, they are not very well known because of the natural variability of material properties. Therefore, the mechanical state can be viewed as a function depending not only on time and space variables but also on material coefficients. This is illustrated in this paper by a sensitivity analysis of the response of a sintering model with respect to variations of material coefficients. The considered variations are defined around an optimized value of coefficients adjusted by experimental results. The proposed method is an incremental method using an extension of the integration scheme developed for the Hyper Reduction method. During the incremental solution, before the adaptation of the representation, an assumed separation representation is used as a reduced-order model. We claim that a truncated integration scheme enables to forecast the reduced-state variables related to the assumed separated representation. The fact that the integrals involved in the formulation can not be written as a sum of products of onedimensional integrals, this approach reduces the extent of the integration domain.

POD–ISAT: An efficient POD‐based surrogate approach with adaptive tabulation and fidelity regions for parametrized steady‐state PDE discrete solutions

“…In some sense, it is a set of local reduced-order models with TRs. The accuracy of the model is controlled via TRs, which prevent from tuning the truncation rank of the low-order bases as can be done in [43]. The reduction of both space and parameters is performed by a combination of the POD method with the ISAT algorithm [19,20], the goal being to cover the whole design parameter with local surrogate models enclosed in TRs.…”

Improving the k-compressibility of Hyper Reduced Order Models with moving sources: Applications to welding and phase change problems

“…For instance, in [17] the extension to nonlinear Finite Element models making use of an a priori approach is presented and the term hyper-reduction is coined to refer to the general procedure of performing a second reduction. Another work following this line is that of Sarbandi et al [18].…”

Numerical Aspects of a Continuum Sintering Model Formulated in the Standard Dissipative Framework

“…Substantial further reductions of computational cost are possible by additionally utilizing classical adaptive schemes like adaptive time stepping and hp-adaptive finite element methods or model order reduction approaches. An example for the use of the latter in the context of sintering simulations can be found in Sarbandi et al [3]. A discussion of such adaptive schemes is, however, beyond the scope of this contribution.…”