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Boto RA, Peccati F, Laplaza R, Quan C, Carbone A, Piquemal JP, Maday Y, Contreras-Garcı A J. NCIPLOT4: Fast, Robust, and Quantitative Analysis of Noncovalent Interactions. J Chem Theory Comput 2020; 16:4150-4158. [PMID: 32470306 DOI: 10.1021/acs.jctc.0c00063] [Citation(s) in RCA: 109] [Impact Index Per Article: 27.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The NonCovalent Interaction index (NCI) enables identification of attractive and repulsive noncovalent interactions from promolecular densities in a fast manner. However, the approach remained up to now qualitative, only providing visual information. We present a new version of NCIPLOT, NCIPLOT4, which allows quantifying the properties of the NCI regions (volume, charge) in small and big systems in a fast manner. Examples are provided of how this new twist enables characterization and retrieval of local information in supramolecular chemistry and biosystems at the static and dynamic levels.
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Stamm B, Lagardère L, Polack É, Maday Y, Piquemal JP. A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms. J Chem Phys 2018; 149:124103. [PMID: 30278683 DOI: 10.1063/1.5044541] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on the expressions of the so-called self-parts of the Ewald summation where different expressions can be found in the literature. Indeed, such expressions are of prime importance in the context of new generation polarizable force field where the self-field appears in the polarization equations. We provide a general framework, where the idea of the Ewald splitting is applied to the electric potential and, subsequently, all other quantities such as the electric field, the energy, and the forces are derived consistently thereof. Mathematical well-posedness is shown for all these contributions for any order of multipolar distribution.
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Lindgren EB, Stamm B, Maday Y, Besley E, Stace AJ. Dynamic simulations of many-body electrostatic self-assembly. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:20170143. [PMID: 29431686 PMCID: PMC5805913 DOI: 10.1098/rsta.2017.0143] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 11/21/2017] [Indexed: 06/08/2023]
Abstract
Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process.This article is part of the theme issue 'Modern theoretical chemistry'.
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Lagardère L, Jolly LH, Lipparini F, Aviat F, Stamm B, Jing ZF, Harger M, Torabifard H, Cisneros GA, Schnieders MJ, Gresh N, Maday Y, Ren PY, Ponder JW, Piquemal JP. Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields. Chem Sci 2018; 9:956-972. [PMID: 29732110 PMCID: PMC5909332 DOI: 10.1039/c7sc04531j] [Citation(s) in RCA: 129] [Impact Index Per Article: 21.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Accepted: 11/24/2017] [Indexed: 12/23/2022] Open
Abstract
We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed.
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Aviat F, Levitt A, Stamm B, Maday Y, Ren P, Ponder JW, Lagardère L, Piquemal JP. Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations. J Chem Theory Comput 2016; 13:180-190. [PMID: 28068773 PMCID: PMC5228058 DOI: 10.1021/acs.jctc.6b00981] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
We
introduce a new class of methods, denoted as Truncated Conjugate
Gradient(TCG), to solve the many-body polarization energy and its
associated forces in molecular simulations (i.e. molecular dynamics
(MD) and Monte Carlo). The method consists in a fixed number of Conjugate
Gradient (CG) iterations. TCG approaches provide a scalable solution
to the polarization problem at a user-chosen cost and a corresponding
optimal accuracy. The optimality of the CG-method guarantees that
the number of the required matrix-vector products are reduced to a
minimum compared to other iterative methods. This family of methods
is non-empirical, fully adaptive, and provides analytical gradients,
avoiding therefore any energy drift in MD as compared to popular iterative
solvers. Besides speed, one great advantage of this class of approximate
methods is that their accuracy is systematically improvable. Indeed,
as the CG-method is a Krylov subspace method, the associated error
is monotonically reduced at each iteration. On top of that, two improvements
can be proposed at virtually no cost: (i) the use of preconditioners
can be employed, which leads to the Truncated Preconditioned Conjugate
Gradient (TPCG); (ii) since the residual of the final step of the
CG-method is available, one additional Picard fixed point iteration
(“peek”), equivalent to one step of Jacobi Over Relaxation
(JOR) with relaxation parameter ω, can be made at almost no
cost. This method is denoted by TCG-n(ω). Black-box adaptive
methods to find good choices of ω are provided and discussed.
Results show that TPCG-3(ω) is converged to high accuracy (a
few kcal/mol) for various types of systems including proteins and
highly charged systems at the fixed cost of four matrix-vector products:
three CG iterations plus the initial CG descent direction. Alternatively,
T(P)CG-2(ω) provides robust results at a reduced cost (three
matrix-vector products) and offers new perspectives for long polarizable
MD as a production algorithm. The T(P)CG-1(ω) level provides
less accurate solutions for inhomogeneous systems, but its applicability
to well-conditioned problems such as water is remarkable, with only
two matrix-vector product evaluations.
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Lipparini F, Lagardère L, Raynaud C, Stamm B, Cancès E, Mennucci B, Schnieders M, Ren P, Maday Y, Piquemal JP. Polarizable molecular dynamics in a polarizable continuum solvent. J Chem Theory Comput 2016; 11:623-34. [PMID: 26516318 DOI: 10.1021/ct500998q] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
We present, for the first time, scalable polarizable molecular dynamics (MD) simulations within a polarizable continuum solvent with molecular shape cavities and exact solution of the mutual polarization. The key ingredients are a very efficient algorithm for solving the equations associated with the polarizable continuum, in particular, the domain decomposition Conductor-like Screening Model (ddCOSMO), which involves a rigorous coupling of the continuum with the polarizable force field achieved through a robust variational formulation and an effective strategy to solve the coupled equations. The coupling of ddCOSMO with nonvariational force fields, including AMOEBA, is also addressed. The MD simulations are feasible, for real-life systems, on standard cluster nodes; a scalable parallel implementation allows for further acceleration in the context of a newly developed module in Tinker, named Tinker-HP. NVE simulations are stable, and long-term energy conservation can be achieved. This paper is focused on the methodological developments, the analysis of the algorithm, and the stability of the simulations; a proof-of-concept application is also presented to attest to the possibilities of this newly developed technique.
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Stamm B, Cancès E, Lipparini F, Maday Y. A new discretization for the polarizable continuum model within the domain decomposition paradigm. J Chem Phys 2016; 144:054101. [DOI: 10.1063/1.4940136] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Lipparini F, Scalmani G, Lagardère L, Stamm B, Cancès E, Maday Y, Piquemal JP, Frisch MJ, Mennucci B. Quantum, classical, and hybrid QM/MM calculations in solution: general implementation of the ddCOSMO linear scaling strategy. J Chem Phys 2015; 141:184108. [PMID: 25399133 DOI: 10.1063/1.4901304] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Abstract
We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.
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Lagardère L, Lipparini F, Polack É, Stamm B, Cancès É, Schnieders M, Ren P, Maday Y, Piquemal JP. Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II. Toward Massively Parallel Computations Using Smooth Particle Mesh Ewald. J Chem Theory Comput 2015; 11:2589-99. [DOI: 10.1021/acs.jctc.5b00171] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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35
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Suárez G, Maday Y, Bustamante J. Mechanical bio-pump as a functional component of a ventricular assist system: haemodynamic-modelling study and fluid-structure solution. INTERNATIONAL JOURNAL OF BIOMEDICAL ENGINEERING AND TECHNOLOGY 2015. [DOI: 10.1504/ijbet.2015.072935] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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36
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Szopos M, Poussineau N, Maday Y, Canniffe C, Celermajer DS, Bonnet D, Ou P. Computational modeling of blood flow in the aorta—insights into eccentric dilatation of the ascending aorta after surgery for coarctation. J Thorac Cardiovasc Surg 2014; 148:1572-82. [DOI: 10.1016/j.jtcvs.2013.11.055] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/22/2013] [Revised: 11/01/2013] [Accepted: 11/15/2013] [Indexed: 12/31/2022]
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37
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Bernardi C, Maday Y, Rapetti F. Basics and some applications of the mortar element method. ACTA ACUST UNITED AC 2014. [DOI: 10.1002/gamm.201490020] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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38
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Lipparini F, Lagardère L, Scalmani G, Stamm B, Cancès E, Maday Y, Piquemal JP, Frisch MJ, Mennucci B. Quantum Calculations in Solution for Large to Very Large Molecules: A New Linear Scaling QM/Continuum Approach. J Phys Chem Lett 2014; 5:953-958. [PMID: 26270973 DOI: 10.1021/jz5002506] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a new implementation of continuum solvation models for semiempirical Hamiltonians that allows the description of environmental effects on very large molecular systems. In this approach based on a domain decomposition strategy of the COSMO model (ddCOSMO), the solution to the COSMO equations is no longer the computational bottleneck but becomes a negligible part of the overall computation time. In this Letter, we analyze the computational impact of COSMO on the solution of the SCF equations for large to very large molecules, using semiempirical Hamiltonians, for both the new ddCOSMO implementation and the most recent, linear scaling one, based on the fast multipole method. A further analysis is on the simulation of the UV/visible spectrum of a light-harvesting pigment-protein complex. All of the results show how the new ddCOSMO algorithm paves the way to routine computations for large molecular systems in the condensed phase.
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39
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Lagardère L, Lipparini F, Polack É, Stamm B, Cancès É, Schnieders M, Ren P, Maday Y, Piquemal JP. Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald. J Chem Theory Comput 2014; 10:1638-1651. [PMID: 26512230 DOI: 10.1021/ct401096t] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.
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40
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Cancès E, Maday Y, Stamm B. Domain decomposition for implicit solvation models. J Chem Phys 2013; 139:054111. [DOI: 10.1063/1.4816767] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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41
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Lipparini F, Stamm B, Cancès E, Maday Y, Mennucci B. Fast Domain Decomposition Algorithm for Continuum Solvation Models: Energy and First Derivatives. J Chem Theory Comput 2013; 9:3637-48. [DOI: 10.1021/ct400280b] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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42
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43
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Maday Y, Cuong Nguyen N, T. Patera A, H. Pau S. A general multipurpose interpolation procedure: the magic points. ACTA ACUST UNITED AC 2009. [DOI: 10.3934/cpaa.2009.8.383] [Citation(s) in RCA: 135] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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44
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Fodil R, Croce C, Louis B, Coste A, Blondeau J, Isabey D, Perchet D, Fetita C, Preteux F, Grenier P, Vial L, Caillibotte G, Till M, Maday Y, Thiriet M, de Rochefort L, Maître X, Bittoun J, Durand E, Sbirlea-Apiou G. Simulateur morphofonctionnel des voies aériennes supérieures et proximales. ACTA ACUST UNITED AC 2005. [DOI: 10.1016/j.rbmret.2004.11.006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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45
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Maday Y, Turinici G. New formulations of monotonically convergent quantum control algorithms. J Chem Phys 2003. [DOI: 10.1063/1.1564043] [Citation(s) in RCA: 137] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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46
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Baffico L, Bernard S, Maday Y, Turinici G, Zérah G. Parallel-in-time molecular-dynamics simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:057701. [PMID: 12513644 DOI: 10.1103/physreve.66.057701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2002] [Indexed: 05/24/2023]
Abstract
While there have been many progress in the field of multiscale simulations in the space domain, in particular, due to efficient parallelization techniques, much less is known in the way to perform similar approaches in the time domain. In this paper we show on two examples that, provided we can describe in a rough but still accurate way the system under consideration, it is indeed possible to parallelize molecular dynamics simulations in time by using the recently introduced pararealalgorithm. The technique is most useful for ab initio simulations.
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47
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Maday Y, Patera A, Rovas D. A Blackbox Reduced-Basis Output Bound Method for Noncoercive Linear Problems. NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS - COLLÈGE DE FRANCE SEMINAR VOLUME XIV 2002. [DOI: 10.1016/s0168-2024(02)80025-x] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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48
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Machiels L, Maday Y, Oliveira IB, Patera AT, Rovas DV. Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems. ACTA ACUST UNITED AC 2000. [DOI: 10.1016/s0764-4442(00)00270-6] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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49
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Machiels L, Maday Y, Patera AT. A “flux-free” nodal Neumann subproblem approach to output bounds for partial differential equations. ACTA ACUST UNITED AC 2000. [DOI: 10.1016/s0764-4442(00)00122-1] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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50
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Maday Y, Patera AT, Peraire J. A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem. ACTA ACUST UNITED AC 1999. [DOI: 10.1016/s0764-4442(99)80279-1] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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