Related papers: Reduced-order computational homogenization for hyp…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
Coarse-scale surrogate models in the context of numerical homogenization of linear elliptic problems with arbitrary rough diffusion coefficients rely on the efficient solution of fine-scale sub-problems on local subdomains whose solutions…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
The usage of numerical homogenization to obtain structure-property relations using the finite element method at both the micro and macroscale has gained much interest in the research community. However the computational cost of this so…
We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macro-energy density.…
This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…
We propose an efficient hyper-reduced order model (HROM) designed for segregated finite-volume solvers in geometrically parametrized problems. The method follows a discretize-then-project strategy: the full-order operators are first…
In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…
A central question in numerical homogenization of partial differential equations with multiscale coefficients is the accurate computation of effective quantities, such as the homogenized coefficients. Computing homogenized coefficients…
We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…
Gradient dominance property is a condition weaker than strong convexity, yet sufficiently ensures global convergence even in non-convex optimization. This property finds wide applications in machine learning, reinforcement learning (RL),…
In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…
In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…
We investigate the use of reduced-order modelling to run discrete element simulations at higher speeds. Taking a data-driven approach, we run many offline simulations in advance and train a model to predict the velocity field from the mass…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…