相关论文: Analysis of two-phase shape optimization problems …

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

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…

This essay, an excerpt of the author's Ph.D. in Philosophy of mathematics (2012) thought of as being a companion to recent discoveries of new explicit Cartan geometry curvatures, analyzes how Gauss, after having devised the isometrically…

The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical…

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…

In this paper we study an abstract framework for computing shape derivatives of functionals subject to PDE constraints. We revisit the Lagrangian approach using the implicit function theorem in an abstract setting tailored for applications…

Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving…

We improve the existing results of optimal partial profile paired choice designs and provide new designs for situations where the choice set sizes are greater than two. The optimal designs are obtained under the main effects models and the…

We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…

In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…

In two phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry…

There are many time series in the literature with high dimension yet limited sample sizes, such as macroeconomic variables, and it is almost impossible to obtain efficient estimation and accurate prediction by using the corresponding…

A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

Shape optimization has been playing an important role in a large variety of engineering applications. Existing shape optimization methods are generally mesh-dependent and therefore encounter challenges due to mesh deformation. To overcome…

In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…

We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…

This paper is concerned with the optimal shape design of the newtonian viscous incompressible fluids driven by the stationary nonhomogeneous Navier-Stokes equations. We use three approaches to derive the structures of shape gradients for…

Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…