Related papers: Adjoint Methods for Guiding Adaptive Mesh Refineme…
We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…
Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is in general difficult due to the…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
We consider computationally expensive blackbox optimization problems and present a method that employs surrogate models and concurrent computing at the search step of the mesh adaptive direct search (MADS) algorithm. Specifically, we solve…
This work presents an optimization framework for tailoring the nonlinear dynamic response of lightly damped mechanical systems using Spectral Submanifold (SSM) reduction. We derive the SSM-based backbone curve and its sensitivity with…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
Medical image analysis relies on accurate segmentation, and benefits from controllable synthesis (of new training images). Yet both tasks of the cyclical pipeline face spatial imbalance: lesions occupy small regions against vast…
This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a…
We consider a shape optimization based method for finding the best interpolation data in the compression of images with noise. The aim is to reconstruct missing regions by means of minimizing a data fitting term in an $L^p$-norm between…
In this paper, the alternating direction method of multipliers (ADMM) is investigated for distributed optimization problems in a networked multi-agent system. In particular, a new adaptive-gain ADMM algorithm is derived in a closed form and…
A discontinuous Galerkin time-domain (DGTD) method based on dynamically adaptive Cartesian meshes (ACM) is developed for a full-wave analysis of electromagnetic fields in dispersive media. Hierarchical Cartesian grids offer simplicity close…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
We have developed a new computer code, RELDAFNA, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. We have implemented a characteristic-wise, finite…
Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR…
We propose a mesh adaptation procedure for Cartesian quadtree meshes, to discretize scalar advection-diffusion-reaction problems. The adaptation process is driven by a recovery-based a posteriori estimator for the $L^2(\Omega)$-norm of the…
We present an adaptive sampling approach to 3D reconstruction of the welding joint using the point cloud that is generated by a laser sensor. We start with a randomized strategy to approximate the surface of the volume of interest through…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
This paper presents a parallel and fully conservative adaptive mesh refinement (AMR) implementation of a finite-volume-based kinetic solver for compressible flows. Time-dependent H-type refinement is combined with a two-population…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…