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We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency.…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
We consider the shape and topology optimization problem to design a structure that minimizes a weighted sum of material consumption and (linearly) elastic compliance under a fixed given boundary load. As is well-known, this problem is in…
This paper applies topology optimisation to the design of structures with periodic microstructural details without length scale separation, i.e. considering the complete macroscopic structure and its response, while resolving all…
Accurate prediction of fracture toughness under complex loading conditions, like mixed mode I/II, is essential for reliable failure assessment. This paper aims to develop a machine learning framework for predicting fracture toughness and…
It is often the case that the computed optimal solution of an optimization problem cannot be implemented directly, irrespective of data accuracy, due to either (i) technological limitations (such as physical tolerances of machines or…
Exact characterization of phase transitions requires sufficient configurational sampling, necessitating efficient and accurate potential energy surfaces. Molecular force fields with computational efficiency and physical interpretability are…
Topology optimization (TO) is a well-established methodology for structural design under user-defined constraints, e.g. minimum volume and maximum stiffness. However, such methods have traditionally been applied to static, deterministic…
Finite element approximations of minimal surface are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element…
Hierarchical optimization refers to problems with interdependent decision variables and objectives, such as minimax and bilevel formulations. While various algorithms have been proposed, existing methods and analyses lack adaptivity in…
This paper presents a Material Mask Overlay topology optimization approach with the improved material assignment at the element level for achieving the desired discreteness of the optimized designs for pressure-loaded problems. Hexagonal…
While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial differential equations with random coefficients enjoy great popularity, combinations with spatial adaptivity seem to be rare. We present an adaptive MLMC…
This paper proposes a computational approach to form-find pin-jointed, bar structures subjected to combinations of tension and compression forces. The generated equilibrium states can meet force and geometric constraints via gradient-based…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
During design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A levelset description of…
We present a learning based framework for mesh quality improvement on unstructured triangular and quadrilateral meshes. Our model learns to improve mesh quality according to a prescribed objective function purely via self-play reinforcement…
Designing metamaterials for extreme mechanical behavior involves the optimal selection of design parameters. However, identifying these optimal parameters through topology optimization (TO) across a large parametric space requires extensive…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…