Related papers: Fluid dynamic shape optimization using self-adapti…
In this paper, we propose a shape optimization pipeline for propeller blades, applied to naval applications. The geometrical features of a blade are exploited to parametrize it, allowing to obtain deformed blades by perturbating their…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares…
Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid. The objective is to minimize the hydrodynamic power…
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…
We consider a new semidefinite programming relaxation for directed edge expansion, which is obtained by adding triangle inequalities to the reweighted eigenvalue formulation. Applying the matrix multiplicative weight update method to this…
In this research, we investigate a general shape optimization problem in which the state equation is expressed using a nonlocal and nonlinear operator. We prove the existence of a minimum point for a functional $F$ defined on the family of…
In this paper, we investigate neural networks applied to multiscale simulations and discuss a design of a novel deep neural network model reduction approach for multiscale problems. Due to the multiscale nature of the medium, the fine-grid…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…
Due to the high computational load of modern numerical simulation, there is a demand for approaches that would reduce the size of discrete problems while keeping the accuracy reasonable. In this work, we present an original algorithm to…
We propose and investigate a mesh deformation technique for PDE constrained shape optimization. Introducing a gradient penalization to the inner product for linearized shape spaces, mesh degeneration can be prevented within the optimization…
Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques can also be applied to an interface identification problem…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
Machine learning pipelines often rely on optimization procedures to make discrete decisions (e.g., sorting, picking closest neighbors, or shortest paths). Although these discrete decisions are easily computed, they break the…
This paper proposes the method to optimize restriction and prolongation operators in the two-grid method. The proposed method is straightforwardly extended to the geometric multigrid method (GMM). GMM is used in solving discretized partial…