Related papers: Fluid dynamic shape optimization using self-adapti…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a…
In this work we present an adaptive Newton-type method to solve nonlinear constrained optimization problems in which the constraint is a system of partial differential equations discretized by the finite element method. The adaptive…
The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such…
Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a proximity operator comes with its structure at no additional cost, and…
In this work we study a general shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze…
A novel methodology to efficiently approximate the Hessian for numerical shape optimization is considered. The method enhances operator symbol approximations by including body fitted coordinates and spatially changing symbols in a semi…
The evolution of dynamical systems is generically governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources. In this work, we present a novel…
In the present chapter we focus on the fundamentals of non-grid-conforming numerical approaches to simulating particulate flows, implementation issues and grid convergence vs. available reference data. The main idea is to avoid adapting the…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
We present a mesh-independent and parameter-robust multigrid solver for the Scott-Vogelius discretisation of the nearly incompressible linear elasticity equations on meshes with a macro element structure. The discretisation achieves exact…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
Sequential implicit (SI) formulations are gaining increasing interest due to their ability to decouple reservoir simulation problems into distinct flow and transport subproblems, allowing for the use of specialized solvers tailored to each.…
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equations, using projection-based reduced-order models accelerated…
We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…