Now showing items 146-165 of 204

• #### A Painless Automatic hp-Adaptive Strategy for Elliptic Problems ﻿

(2020-01)
In this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical ...
• #### Parallel refined Isogeometric Analysis in 3D ﻿

(2018-11)
We study three-dimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p-1}$ basis functions, which provide multiple benefits ...
• #### Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form ﻿

(2015-12-31)
We present an efficient numerical method for computing Fourier-Taylor expansions of (un)stable manifolds associated with hyperbolic periodic orbits. Three features of the method are that (1) we obtain accurate representation ...
• #### Performance of a multi-frontal parallel direct solver for hp-finite element method ﻿

(2009-12-31)
In this paper we present the performance of our parallel multi-frontal direct solver when applied to solve linear systems of equations resulting from discretizations of a hp Finite Element Method (hp-FEM). The hp-FEM ...
• #### PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces ﻿

(2017-01)
We describe a high-performance solution framework for isogeometric discrete differential forms based on B-splines: PetIGA-MF. Built on top of PetIGA, an open-source library we have built and developed over the last decade, ...
• #### A posteriori error analysis of a stabilized mixed FEM for convectuion-diffusion problems ﻿

(2015-12-31)
We present an augmented dual-mixed variational formulation for a linear convection-diffusion equation with homogeneous Dirichlet boundary conditions. The approach is based on the addition of suitable least squares type ...
• #### A posteriori error analysis of an augmented mixed finite element method for Darcy flow ﻿

(2015-12-31)
We develop an a posteriori error analysis of residual type of a stabilized mixed finite element method for Darcy flow. The stabilized formulation is obtained by adding to the standard dual-mixed approach suitable residual ...
• #### A Quadrature-Free Method for Simulation and Inversion of 1.5D Direct Current (DC) Borehole Measurements ﻿

(2016-12)
Resistivity inverse problems are routinely solved in order to characterize hydrocarbon bearing formations. They often require a large number of forward problems simulations. When considering a one dimensional (1D) planarly ...
• #### Quantities of interest for surface based resistivity geophysical measurements ﻿

(2015-12-31)
The objective of traditional goal-oriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical ...
• #### Rational approximation of P-wave kinematics — Part 1: Transversely isotropic media ﻿

(2020-09)
In seismic data processing and several wave propagation modeling algorithms, the phase velocity, group velocity, and traveltime equations are essential. To have these equations in explicit form, or to reduce algebraic ...
• #### Rational approximation of P-wave kinematics — Part 2: Orhorhombic media ﻿

(2020-09)
Orthorhombic anisotropy is a modern standard for 3D seismic studies in complex geologic settings. Several seismic data processing methods and wave propagation modeling algorithms in orthorhombic media rely on phase-velocity, ...
• #### Red refinements of simplices into congruent subsimplices ﻿

(2014-12-31)
We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which ...
• #### Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver ﻿

(2018-06-15)
Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces $C^0$ hyperplanes that act as separators for the direct LU factorization solver. As a result, ...
• #### Refined Isogeometric Analysis for fluid mechanics and electromagnetism ﻿

(2019-03)
Starting from a highly continuous isogeometric analysis discretization, we introduce hyperplanes that partition the domain into subdomains and reduce the continuity of the discretization spaces at these hyperplanes. As the ...
• #### Refined isogeometric analysis for generalized Hermitian eigenproblems ﻿

(2021-04)
We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution ...
• #### Refined isogeometric analysis of quadratic eigenvalue problems ﻿

(2022-07-16)
Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while ...
• #### REFINED ISOGEOMETRIC ANALYSIS: A SOLVER-BASED DISCRETIZATION METHOD ﻿

(2018-06-22)
Isogeometric analysis (IGA) is a computational approach frequently employed nowadays to study problems governed by partial differential equations (PDEs). This approach defines the geometry using conventional computer-aided ...
• #### Regions of prevalence in the coupled restricted three-body problems approximation ﻿

(2012-12-31)
This work concerns the role played by a couple of the planar circular restricted three-body problem in the approximation of the bicircular model. The comparison between the differential equations governing the dynamics ...
• #### Regular polygons on isochordal-viewed hedgehogs ﻿

(2022)
A curve $\alpha$ is called isochordal viewed if there is a smooth motion of a constant length chord with its endpoints along $\alpha$ such that their tangents to the curve at these points form a constant angle. In this ...
• #### Reparameterization of ruled surfaces: toward generating smooth jerk-minimized toolpaths for multi-axis flank CNC milling ﻿

(2020-05)
This paper presents a novel jerk minimization algorithm in the context of multi-axis flank CNC machining. The toolpath of the milling axis in a flank milling process, a ruled surface, is reparameterized by a B-spline ...