Related papers: Mesh Refinement Method for Solving Optimal Control…
Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…
Stagnation detection has been proposed as a mechanism for randomized search heuristics to escape from local optima by automatically increasing the size of the neighborhood to find the so-called gap size, i.e., the distance to the next…
Recent low-thrust space missions have highlighted the importance of designing trajectories that are robust against uncertainties. In its complete form, this process is formulated as a nonlinear constrained stochastic optimal control…
In the context of numerical solution of PDEs, dynamic mesh redistribution methods (r-adaptive methods) are an important procedure for increasing the resolution in regions of interest, without modifying the connectivity of the mesh. Key to…
Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh…
In many applications, piecewise continuous functions are commonly interpolated over meshes. However, accurate high-order manipulations of such functions can be challenging due to potential spurious oscillations known as the Gibbs phenomena.…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
Reconstructing real-world objects from multi-view images is essential for applications in 3D editing, AR/VR, and digital content creation. Existing methods typically prioritize either geometric accuracy (Multi-View Stereo) or photorealistic…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
Current mesh reduction techniques, while numerous, all primarily reduce mesh size by successive element deletion (e.g. edge collapses) with the goal of geometric and topological feature preservation. The choice of geometric error used to…
The paper describes a continuous second-variation algorithm to solve optimal control problems where the control is defined on a closed set. A second order expansion of a Lagrangian provides linear updates of the control to construct a…
The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only the evaluation of the potential at…
Multi-revolution low-thrust trajectory optimization problems are important and challenging in space mission design. In this paper, an efficient, accurate, and widely applicable pseudospectral method is proposed to solve multi-revolution…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
This paper investigates optimal control problems formulated over a class of piecewise-smooth vector fields. Instead of optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of…
Direct mesh editing and deformation are key components in the geometric modeling and animation pipeline. Mesh editing methods are typically framed as optimization problems combining user-specified vertex constraints with a regularizer that…
Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To…
We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…
This paper addresses a new class of optimal control problems for perturbed sweeping processes with measurable controls in additive perturbations of the dynamics and smooth controls in polyhedral moving sets. We develop a constructive…