Now showing items 41-60 of 205

• #### Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling ﻿

(2013-12-31)
Discrete nonnegativity principles are established for finite element approximations of nonlinear parabolic PDE systems with mixed boundary conditions. Previous results of the authors are extended such that diagonal dominance ...
• #### Dispersion-minimizing quadrature rules for $C^1$ quadratic isogeometric analysis ﻿

(2017-09-20)
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ...
• #### The DPG Method for the Convection-Reaction Problem, Revisited ﻿

(2022-01-01)
We study both conforming and non-conforming versions of the practical DPG method for the convection-reaction problem. We determine that the most common approach for DPG stability analysis - construction of a local Fortin ...
• #### A DPG-based time-marching scheme for linear hyperbolic problems ﻿

(2020-11)
The Discontinuous Petrov-Galerkin (DPG) method is a widely employed discretization method for Partial Di fferential Equations (PDEs). In a recent work, we applied the DPG method with optimal test functions for the time ...
• #### Editors' preface for the topical issue "Advances in Numerical Analysis and Numerical Linear Algebra" ﻿

(2012-12-31)
[No abstract available]
• #### Editors' preface for the topical issue "Numerical Methods for Large-Scale Scientific Computing, I" ﻿

(2013-12-31)
[No abstract available]
• #### Editors' preface for the topical issue "Numerical Methods for Large-Scale Scientific Computing, II" ﻿

(2013-12-31)
[No abstract available]
• #### Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion ﻿

(2020-06)
We present a displacement-based and a mixed isogeometric collocation (IGA-C) formulation for free-form, three-dimensional, shear-deformable beams with high and rapidly-varying curvature and torsion. When such complex shapes ...
• #### Efficient 5-axis CNC trochoidal flank milling of 3D cavities using custom-shaped cutting tools ﻿

(2022-05)
A novel method for trochoidal flank milling of 3D cavities bounded by free-form surfaces is proposed. Existing 3D trochoidal milling methods use on-market milling tools whose shape is typically cylindrical or conical, and ...
• #### Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for B-splines ﻿

(2019-12-14)
Calabr{\`o} et al. [10] changed the paradigm of the mass and stiffness computation from the traditional element-wise assembly to a row-wise concept, showing that the latter one offers integration that may be orders of ...
• #### Efficient quadrature rules for subdivision surfaces in isogeometric analysis ﻿

(2018-10)
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
• #### Efficient rigorous numerics for higher-dimensional PDEs via one-dimensional estimates ﻿

(2013-12-31)
We present an efficient rigorous computational method which is an extension of the work Analytic Estimates and Rigorous Continuation for Equilibria of Higher-Dimensional PDEs (M. Gameiro and J.-P. Lessard, J. Differential ...
• #### Energy-norm-based and goal-oriented automatic hp adaptivity for electromagnetics: Application to waveguide Discontinuities ﻿

(2008-12-31)
The finite-element method (FEM) enables the use of adapted meshes. The simultaneous combination of h (local variations in element size) and p (local variations in the polynomial order of approximation) refinements, i.e., ...
• #### Enhanced variational image dehazing ﻿

(2015-12-31)
Images obtained under adverse weather conditions, such as haze or fog, typically exhibit low contrast and faded colors, which may severely limit the visibility within the scene. Unveiling the image structure under the haze ...
• #### Equivalence between the DPG method and the Exponential Integrators for linear parabolic problems ﻿

(2020-11)
The Discontinuous Petrov-Galerkin (DPG) method and the exponential integrators are two well established numerical methods for solving Partial Di fferential Equations (PDEs) and sti ff systems of Ordinary Di fferential ...
• #### Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements ﻿

(2020-11)
Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of ...
• #### Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements ﻿

(2020-05)
Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of ...
• #### Error representation of the time-marching DPG scheme ﻿

(2022-03-01)
In this article, we introduce an error representation function to perform adaptivity in time of the recently developed time-marching Discontinuous Petrov–Galerkin (DPG) scheme. We first provide an analytical expression for ...
• #### Existence of secondary bifurcations or isolas for PDEs ﻿

(2011-12-31)
In this paper, we introduce a method to conclude about the existence of secondary bifurcations or isolas of steady state solutions for parameter dependent nonlinear partial differential equations. The technique combines ...
• #### Explicit-in-Time Goal-Oriented Adaptivity ﻿

(2019-04-15)
Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ...