31. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation
    2008/02/02 by Berk Hess, Carsten Kutzner, David van der Spoel +1 · 16,097 citations
    Biochemistry, Genetics and Molecular Biology · Chemistry · Materials Science · #Protein Structure and Dynamics #Mass Spectrometry Techniques and Applications #Machine Learning in Materials Science #Computer science #Scalability #Algorithm #Computational science #Node (physics) #Molecular dynamics #Parallel computing #Supercomputer #Domain decomposition methods #Solver #Chemistry
32. A numerical Schrödinger–Poisson solver for radially symmetric nanowire core–shell structures
    2006/11/01 by Lingquan Wang, Deli Wang, Peter M. Asbeck +1 · 49 citations
    Engineering · Mathematics · #Advancements in Semiconductor Devices and Circuit Design #Boundary value problem #Capacitance #Materials science #Mathematical analysis #Mathematics #Nanowire #Nanowire Synthesis and Applications #Physics #Poisson's equation #Quantum mechanics #Schrödinger equation #Semiconductor materials and devices #Shell (structure) #Solver
33. Simulating Radiating and Magnetized Flows in Multiple Dimensions with ZEUS‐MP
    2005/11/30 by John C. Hayes, J. C. Hayes, M. L. Norman +12 · 321 citations
    Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #Computational science #Computer science #Magnetic field #Magnetohydrodynamics #Nuclear reactor physics and engineering #Optics #Parallel computing #Physics #Solar and Space Plasma Dynamics #Solver #ZEUS (particle detector) #astro-ph
34. SUNDIALS
    2005/09/01 by Alan C. Hindmarsh, A.C. Hindmarsh, Peter N. Brown +7 · 2,607 citations
    Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Computational science #Computer science #Mathematics #Matrix Theory and Algorithms #Nonlinear system #Numerical methods for differential equations #Parallel computing #Programming language #Robustness (evolution) #Solver
35. SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
    2005/01/01 by Philip E. Gill, Walter Murray, Michael A. Saunders · 2,855 citations
    Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Algorithm #Applied mathematics #Augmented Lagrangian method #Broyden–Fletcher–Goldfarb–Shanno algorithm #Computer science #Constrained optimization #Constraint (computer-aided design) #Degrees of freedom (physics and chemistry) #Hessian matrix #Mathematical optimization #Mathematics #Nonlinear programming #Nonlinear system #Quadratic equation #Quadratic programming #Reservoir Engineering and Simulation Methods #Sequential quadratic programming #Solver #Trust region
36. A Hybrid Cosmological Hydrodynamic/N‐Body Code Based on a Weighted Essentially Nonoscillatory Scheme
    2004/03/31 by Long‐Long Feng, Long-Long Feng, Chi-Wang Shu +3 · 56 citations
    Engineering · Physics and Astronomy · #Code (set theory) #Computational Fluid Dynamics and Aerodynamics #Convergence (economics) #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Piecewise #Rate of convergence #Shock (circulatory) #Shock tube #Shock wave #Solver #Total variation diminishing #astro-ph
37. Beyond Flux‐limited Diffusion: Parallel Algorithms for Multidimensional Radiation Hydrodynamics
    2002/07/11 by John C. Hayes, Michael L. Norman · 111 citations
    Engineering · Physics and Astronomy · #Code (set theory) #Computation #Computational Fluid Dynamics and Aerodynamics #Context (archaeology) #Cosmology and Gravitation Theories #Non-equilibrium thermodynamics #Opacity #Solar and Space Plasma Dynamics #Solver #Tensor (intrinsic definition) #Variable (mathematics) #astro-ph
38. Reformulation of Smoothed Particle Hydrodynamics with Riemann Solver
    2002/06/01 by Shu‐ichiro Inutsuka, Shu-ichiro Inutsuka · 232 citations
    Engineering · Mathematics · Physics and Astronomy · #Action (physics) #Applied mathematics #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Equations of motion #Fluid Dynamics Simulations and Interactions #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Physics #Riemann hypothesis #Riemann problem #Riemann solver #Smoothed-particle hydrodynamics #Smoothing #Solver #astro-ph
39. Hyperbolic Divergence Cleaning for the MHD Equations
    2002/01/01 by Andreas Dedner, A. Dedner, F. Kemm +6 · 1,307 citations
    Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Computational Fluid Dynamics and Aerodynamics #Conservation law #Constraint (computer-aided design) #Divergence (linguistics) #Geometry #Lagrange multiplier #Magnetic confinement fusion research #Magnetic field #Magnetohydrodynamic drive #Magnetohydrodynamics #Mathematical analysis #Mathematical optimization #Mathematics #Momentum (technical analysis) #Physics #Solver
40. A BVP solver based on residual control and the Maltab PSE
    2001/09/01 by Jacek Kierzenka, Jacek A. Kierzenka, Lawrence F. Shampine +1 · 695 citations
    Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Boundary value problem #Computational Fluid Dynamics and Aerodynamics #Computational science #Computer science #Differential equation #MATLAB #Mathematical analysis #Mathematical optimization #Mathematics #Numerical methods for differential equations #Ode #Ordinary differential equation #Programming language #Residual #Software #Solver
41. Simulating self-gravitating hydrodynamic flows
    1994/02/28 by Ewald Mueller, Ewald Müller, Matthias Steinmetz · 109 citations
    Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Classical mechanics #Computational Fluid Dynamics and Aerodynamics #Computer science #Gas Dynamics and Kinetic Theory #Geophysics and Gravity Measurements #Mathematical analysis #Mathematical optimization #Mathematics #Physics #Poisson distribution #Poisson's equation #Scheme (mathematics) #Solver #Spherical coordinate system #Spherical harmonics #Vector spherical harmonics #Zonal spherical harmonics #astro-ph
42. VODE: A Variable-Coefficient ODE Solver
    1989/09/01 by Peter N. Brown, George D. Byrne, Alan C. Hindmarsh +1 · 1,646 citations
    Computer Science · Mathematics · #Algorithm #Applied mathematics #Coefficient matrix #Computer science #Differential Equations and Numerical Methods #Iterated function #Jacobian matrix and determinant #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Numerical methods for differential equations #Ode #Physics #Solver #Variable (mathematics)
43. On Godunov-Type Methods for Gas Dynamics
    1988/04/01 by Bernd Einfeldt · 1,023 citations
    Engineering · Mathematics · #Applied mathematics #Compressibility #Compressible flow #Computational Fluid Dynamics and Aerodynamics #Discontinuity (linguistics) #Finite volume method #Gas Dynamics and Kinetic Theory #Godunov's scheme #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Numerical analysis #Numerical methods in inverse problems #Numerical stability #Physics #Riemann hypothesis #Riemann problem #Riemann solver #Roe solver #Solver
44. A collocation solver for mixed order systems of boundary value problems
    1979/01/01 by U. Ascher, Uri M. Ascher, J. Christiansen +2 · 556 citations
    Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Applied mathematics #Boundary value problem #Collocation (remote sensing) #Collocation method #Computer science #Differential equation #Iterative Methods for Nonlinear Equations #Mathematical analysis #Mathematical optimization #Mathematics #Nonlinear system #Numerical methods for differential equations #Ordinary differential equation #Solver #Spline (mechanical)
45. Numerical analysis of blood flow in the heart
    1977/11/01 by Charles S. Peskin, Charles S Peskin · 2,568 citations
    Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Boundary (topology) #Boundary value problem #Combinatorics #Computer science #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Immersed boundary method #Laplace transform #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematical optimization #Mathematics #Mechanics #Navier–Stokes equations #Nonlinear system #Physics #Representation (politics) #Solver #Topology (electrical circuits)
46. Strips: A new approach to the application of theorem proving to problem solving
    1971/12/01 by Richard E. Fikes, Richard Fikes, Nils J. Nilsson · 4,082 citations
    Computer Science · Mathematics · #Algebra over a field #Algorithm #Artificial intelligence #Automated theorem proving #Boolean satisfiability problem #Calculus (dental) #Computer science #Discrete mathematics #First-order logic #Formal Methods in Verification #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematical optimization #Mathematics #Problem solver #Pure mathematics #Resolution (logic) #STRIPS #Sequence (biology) #Solver

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