相关论文: Fireshape: a shape optimization toolbox for Firedr…

The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…

For an educational purpose we develop the Python package AutoFreeFem which generates all ingredients for shape optimization with non-linear multi-physics in FreeFEM++ and also outputs the expressions for use in LaTex. As an input, the…

We present a cut finite element method for shape optimization in the case of linear elasticity. The elastic domain is defined by a level-set function, and the evolution of the domain is obtained by moving the level-set along a velocity…

Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…

Several real-world optimization problems involve mixed-variable search spaces, where continuous, ordinal, and categorical decision variables coexist. However, most population-based metaheuristic algorithms are designed for either continuous…

Nature-inspired algorithms are among the most powerful algorithms for optimization. This paper intends to provide a detailed description of a new Firefly Algorithm (FA) for multimodal optimization applications. We will compare the proposed…

The implementation process of a $\texttt{RestrictedFunctionSpace}$ class in Firedrake, a Python library which numerically solves partial differential equations through the use of the finite element method, is documented. This includes an…

This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\'ezier tetrahedra. The…

When solving a PDE problem numerically, a certain mesh-refinement process is always implicit, and very classically, mesh adaptivity is a very effective means to accelerate grid convergence. Similarly, when optimizing a shape by means of an…

We present an initial implementation of a probabilistic PDE-constrained shape optimization algorithm. Our method is based on a novel probabilistic representation of the shape derivative, which is evaluated using Monte Carlo sampling; and…

Computational meshes, as a way to partition space, form the basis of much of PDE simulation technology, for instance for the finite element and finite volume discretization methods. In complex simulations, we are often driven to modify an…

Creating scalable, high performance PDE-based simulations requires a suitable combination of discretizations, differential operators, preconditioners and solvers. The required combination changes with the application and with the available…

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free…

Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of partial differential equations (PDEs). This paper describes…

We present a differentiable weak-form learning approach for accelerating finite element simulations. Rather than introducing black-box source terms in the strong form of the governing equations, we augment the momentum equation directly in…

Software development effort estimation is considered a fundamental task for software development life cycle as well as for managing project cost, time and quality. Therefore, accurate estimation is a substantial factor in projects success…

The divertor in a magnetic confinement fusion reactor is an essential component for power dissipation and particle removal. The FIREFLY package for rapid evaluation of divertor designs is presented as an extension of the FLARE code for…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

An emerging theme across many domains of science and engineering is materials that change shape, often dramatically. Determining their structure involves solving a shape optimization problem where a given energy functional is minimized with…

In this paper, we propose an unfitted finite element method to solve PDE-constrained shape optimization problems via shape gradient flow. The shape gradient flow system consists of the state equation, the adjoint equation, the velocity…