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We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are…
The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial…
Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures, a novel asymptotic homogenisation topology optimisation…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or…
We derive a mixture theory-based mathematical model of the degradation of a poroelastic solid immersed in a fluid bath. The evolution of the solid's mechanical and transport properties are also modeled. The inspiration for the model is the…
This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…
Engineers manually optimizing a structure using Finite Element based simulation software often employ an iterative approach where in each iteration they change the structure slightly and resimulate. Standard Finite Element based simulation…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…
We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…
We propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the…
In this paper, we consider a time-dependent discrete network model with highly varying connectivity. The approximation by time is performed using an implicit scheme. We propose the coarse scale approximation construction of network models…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
Time domain simulations of electromagnetic problems are highly valuable in engineering applications, as they allow for the analysis of transient behavior and broadband responses. These simulations utilize time stepping schemes, where each…
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for biharmonic equations with built-in stabilizers. Unlike existing stabilizer-free WG methods limited to convex elements in finite element partitions, our…
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite…
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…