Browsing by Author "Calo, V.M."
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Computational cost estimates for parallel shared memory isogeometric multifrontal solvers
Wozniak, M.; Kuznik, K.; Paszynski, M.; Calo, V.M.; Pardo, D. (20141231)In this paper we present computational cost estimates for parallel shared memory isogeometric multifrontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as $\mathcal{O}( ... 
Computational cost of isogeometric multifrontal solvers on parallel distributed memory machines
Wozniak, M.; Paszynski, M.; Pardo, D.; Dalcin, L.; Calo, V.M. (20151231)This paper derives theoretical estimates of the computational cost for isogeometric multifrontal direct solver executed on parallel distributed memory machines. We show theoretically that for the $C^{p1}$ global continuity ... 
Direct solvers performance on hadapted grids
Paszynski, M.; Pardo, D.; Calo, V.M. (20151231)We analyse the performance of direct solvers when applied to a system of linear equations arising from an $h$adapted, $C^0$ finite element space. Theoretical estimates are derived for typical $h$refinement patterns arising ... 
Dispersionminimizing quadrature rules for $C^1$ quadratic isogeometric analysis
Deng, Q.; Barton, M.; Puzyrev, V.; Calo, V.M. (20170920)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 ... 
Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for Bsplines
Barton, M.; Puzyrev, V.; Deng, Q.; Calo, V.M. (20191214)Calabr{\`o} et al. [10] changed the paradigm of the mass and stiffness computation from the traditional elementwise assembly to a rowwise concept, showing that the latter one offers integration that may be orders of ... 
Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements
Shahriari, M.; Pardo, D.; Rivera, J.A.; TorresVerdín, C.; Picon, A.; Ossandón, S.; Calo, V.M.; Del Ser, J. (202011)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 ... 
ExplicitinTime GoalOriented Adaptivity
MuñozMatute, J.; Calo, V.M.; Pardo, D.; Alberdi, E.; Van der Zee, K.G. (20190415)Goaloriented 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 ... 
ForwardinTime GoalOriented Adaptivity
MuñozMatute, J.; Pardo, D.; Calo, V.M.; Alberdi, E. (201903)In goaloriented adaptive algorithms for partial differential equations, we adapt the finite element mesh in order to reduce the error of the solution in some quantity of interest. In timedependent problems, this adaptive ... 
GaussGalerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
Barton, M.; Calo, V.M. (20160701)We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature ... 
Gaussian quadrature rules for $C^1$ quintic splines with uniform knot vectors
Barton, M.; AitHaddou, R.; Calo, V.M. (20170322)We provide explicit quadrature rules for spaces of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. ... 
Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis
Barton, M.; Calo, V.M.; Deng, Q.; Puzyrev, V. (20181013)This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ... 
ICCS 2017 Workshop on AgentBased Simulations, Adaptive Algorithms and Solvers
Byrski, A.; Paszynski, M.; Schaefer, R.; Calo, V.M.; Pardo, D. (2017)This workshop seeks to integrate results from different domains of computer science, computational science, and mathematics. We welcome simulation papers, either hard simulations using finite element or finite difference ... 
A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
Shahriari, M.; Rojas, S.; Pardo, D.; RodríguezRozas, A.; Bakr, S.A.; Calo, V.M.; Muga, I. (20180614)In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ... 
Optimal quadrature rules for odddegree spline spaces and their application to tensorproductbased isogeometric analysis
Barton, M.; Calo, V.M. (20160101)We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Barton and Calo, 2016) that ... 
Parallel refined Isogeometric Analysis in 3D
Siwik, L.; Wozniak, M.; Trujillo, V.; Pardo, D.; Calo, V.M.; Paszynski, M. (201811)We study threedimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p1}$ basis functions, which provide multiple benefits ... 
PetIGAMF: A multifield highperformance toolbox for structurepreserving Bsplines spaces
Sarmiento, A.F.; Côrtes , A.M.A.; Garcia, D.; Dalcin, L.; Collier, N.; Calo, V.M. (201701)We describe a highperformance solution framework for isogeometric discrete differential forms based on Bsplines: PetIGAMF. Built on top of PetIGA, an opensource library we have built and developed over the last decade, ... 
Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver
Garcia, D.; Pardo, D.; Dalcin, L.; Calo, V.M. (20180615)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
Garcia, D.; Pardo, D.; Calo, V.M. (201903)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
Hashemian, A.; Pardo, D.; Calo, V.M. (202104)We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximumcontinuity isogeometric analysis (IGA) while it reduces the solution ... 
TimeDomain GoalOriented Adaptivity Using PseudoDual Error Representations
MuñozMatute, J.; Alberdi, E.; Pardo, D.; Calo, V.M. (201712)Goaloriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudodual problems for goaloriented adaptivity in the ...