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papers.bib
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@article{brezzi_existence_1974,
title = {On the existence, uniqueness and approximation of saddle-point problems arising from {Lagrangian} multipliers},
volume = {8},
number = {2},
journal = {RAIRO Anal. Numer},
author = {Brezzi, F.},
year = {1974},
pages = {129--151},
}
@book{hestenes_methods_1952,
title = {Methods of conjugate gradients for solving linear systems},
volume = {49},
number = {1},
publisher = {NBS Washington, DC},
author = {Hestenes, Magnus Rudolph and Stiefel, Eduard},
year = {1952},
file = {Full Text:/Users/jack.hale/Zotero/storage/4QDJZIKG/Hestenes and Stiefel - 1952 - Methods of conjugate gradients for solving linear .pdf:application/pdf},
}
@article{brandt_multi-level_1977,
title = {Multi-{Level} {Adaptive} {Solutions} to {Boundary}-{Value} {Problems}},
volume = {31},
issn = {0025-5718},
url = {https://www.jstor.org/stable/2006422},
doi = {10.2307/2006422},
abstract = {The boundary-value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes. Interactions between these levels enable us (i) to solve the possibly nonlinear system of \$n\$ discrete equations in \$O(n)\$ operations (\$40n\$ additions and shifts for Poisson problems); (ii) to conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "\${\textbackslash}infty\$-order" approximations and low \$n\$, even when singularities are present. General theoretical analysis of the numerical process. Numerical experiments with linear and nonlinear, elliptic and mixed-type (transonic flow) problems--confirm theoretical predictions. Similar techniques for initial-value problems are briefly discussed.},
number = {138},
urldate = {2021-07-07},
journal = {Mathematics of Computation},
author = {Brandt, Achi},
year = {1977},
note = {Publisher: American Mathematical Society},
pages = {333--390},
file = {Full Text:/Users/jack.hale/Zotero/storage/9F4L4F8N/Brandt - 1977 - Multi-Level Adaptive Solutions to Boundary-Value P.pdf:application/pdf},
}
@article{de_boor_calculating_1972,
title = {On calculating with {B}-splines},
volume = {6},
issn = {0021-9045},
url = {https://www.sciencedirect.com/science/article/pii/0021904572900809},
doi = {10.1016/0021-9045(72)90080-9},
language = {en},
number = {1},
urldate = {2021-07-07},
journal = {Journal of Approximation Theory},
author = {de Boor, Carl},
month = jul,
year = {1972},
pages = {50--62},
file = {ScienceDirect Full Text PDF:/Users/jack.hale/Zotero/storage/TJ5S5PGA/de Boor - 1972 - On calculating with B-splines.pdf:application/pdf;ScienceDirect Snapshot:/Users/jack.hale/Zotero/storage/HW6QSUN7/0021904572900809.html:text/html},
}
@article{cooley_algorithm_1965,
title = {An {Algorithm} for the {Machine} {Calculation} of {Complex} {Fourier} {Series}},
volume = {19},
issn = {0025-5718},
url = {https://www.jstor.org/stable/2003354},
doi = {10.2307/2003354},
number = {90},
urldate = {2021-07-07},
journal = {Mathematics of Computation},
author = {Cooley, James W. and Tukey, John W.},
year = {1965},
note = {Publisher: American Mathematical Society},
pages = {297--301},
file = {Full Text:/Users/jack.hale/Zotero/storage/RWE4YF5Y/Cooley and Tukey - 1965 - An Algorithm for the Machine Calculation of Comple.pdf:application/pdf},
}
@article{golub_calculation_1969,
title = {Calculation of {Gauss} {Quadrature} {Rules}},
volume = {23},
issn = {0025-5718},
url = {https://www.jstor.org/stable/2004418},
doi = {10.2307/2004418},
abstract = {Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for computing the three term recurrence relation from the moments of the weight function.},
number = {106},
urldate = {2021-07-07},
journal = {Mathematics of Computation},
author = {Golub, Gene H. and Welsch, John H.},
year = {1969},
note = {Publisher: American Mathematical Society},
pages = {221--s10},
file = {Full Text:/Users/jack.hale/Zotero/storage/5JATEFB6/Golub and Welsch - 1969 - Calculation of Gauss Quadrature Rules.pdf:application/pdf},
}
@article{broyden_class_1965,
title = {A class of methods for solving nonlinear simultaneous equations},
volume = {19},
issn = {0025-5718, 1088-6842},
url = {https://www.ams.org/mcom/1965-19-092/S0025-5718-1965-0198670-6/},
doi = {10.1090/S0025-5718-1965-0198670-6},
abstract = {Advancing research. Creating connections.},
language = {en},
number = {92},
urldate = {2021-07-07},
journal = {Mathematics of Computation},
author = {Broyden, C. G.},
year = {1965},
pages = {577--593},
file = {Full Text PDF:/Users/jack.hale/Zotero/storage/V26Q3SID/Broyden - 1965 - A class of methods for solving nonlinear simultane.pdf:application/pdf;Snapshot:/Users/jack.hale/Zotero/storage/3FBYEDVX/home.html:text/html},
}
@article{butcher_history_1996,
title = {A history of {Runge}-{Kutta} methods},
volume = {20},
issn = {0168-9274},
url = {https://www.sciencedirect.com/science/article/pii/0168927495001085},
doi = {10.1016/0168-9274(95)00108-5},
abstract = {This paper constitutes a centenary survey of Runge-Kutta methods. It reviews some of the early contributions due to Runge, Heun, Kutta and Nyström and leads on to the theory of order of accuracy of Runge-Kutta methods, and includes a discussion of implicit methods, stability analysis and methods of error estimation and dense output.},
language = {en},
number = {3},
urldate = {2021-07-07},
journal = {Applied Numerical Mathematics},
author = {Butcher, J. C.},
month = mar,
year = {1996},
pages = {247--260},
file = {ScienceDirect Snapshot:/Users/jack.hale/Zotero/storage/LQF9K5BC/0168927495001085.html:text/html},
}
@article{higham_accuracy_1993,
title = {The {Accuracy} of {Floating} {Point} {Summation}},
volume = {14},
issn = {1064-8275, 1095-7197},
url = {http://epubs.siam.org/doi/10.1137/0914050},
doi = {10.1137/0914050},
language = {en},
number = {4},
urldate = {2021-07-07},
journal = {SIAM Journal on Scientific Computing},
author = {Higham, Nicholas J.},
month = jul,
year = {1993},
pages = {783--799},
}
@article{saad_gmres_1986,
title = {{GMRES}: {A} {Generalized} {Minimal} {Residual} {Algorithm} for {Solving} {Nonsymmetric} {Linear} {Systems}},
volume = {7},
issn = {0196-5204},
shorttitle = {{GMRES}},
url = {https://epubs.siam.org/doi/abs/10.1137/0907058},
doi = {10.1137/0907058},
abstract = {We present an iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace. The algorithm is derived from the Arnoldi process for constructing an \$l\_2 \$-orthogonal basis of Krylov subspaces. It can be considered as a generalization of Paige and Saunders’ MINRES algorithm and is theoretically equivalent to the Generalized Conjugate Residual (GCR) method and to ORTHODIR. The new algorithm presents several advantages over GCR and ORTHODIR.},
number = {3},
urldate = {2021-07-07},
journal = {SIAM Journal on Scientific and Statistical Computing},
author = {Saad, Youcef and Schultz, Martin H.},
month = jul,
year = {1986},
note = {Publisher: Society for Industrial and Applied Mathematics},
pages = {856--869},
file = {Snapshot:/Users/jack.hale/Zotero/storage/NS7JT3TY/0907058.html:text/html;Submitted Version:/Users/jack.hale/Zotero/storage/7L8WXCM6/Saad and Schultz - 1986 - GMRES A Generalized Minimal Residual Algorithm fo.pdf:application/pdf},
}
@article{gustafson_reevaluating_1988,
title = {Reevaluating {Amdahl}'s law},
volume = {31},
issn = {0001-0782},
url = {https://doi.org/10.1145/42411.42415},
doi = {10.1145/42411.42415},
number = {5},
urldate = {2021-07-07},
journal = {Communications of the ACM},
author = {Gustafson, John L.},
month = may,
year = {1988},
pages = {532--533},
}
@article{lamport_time_1978,
title = {Time, clocks, and the ordering of events in a distributed system},
volume = {21},
issn = {0001-0782},
url = {https://doi.org/10.1145/359545.359563},
doi = {10.1145/359545.359563},
abstract = {The concept of one event happening before another in a distributed system is examined, and is shown to define a partial ordering of the events. A distributed algorithm is given for synchronizing a system of logical clocks which can be used to totally order the events. The use of the total ordering is illustrated with a method for solving synchronization problems. The algorithm is then specialized for synchronizing physical clocks, and a bound is derived on how far out of synchrony the clocks can become.},
number = {7},
urldate = {2021-07-07},
journal = {Communications of the ACM},
author = {Lamport, Leslie},
month = jul,
year = {1978},
keywords = {clock synchronization, computer networks, distributed systems, multiprocess systems},
pages = {558--565},
file = {Full Text:/Users/jack.hale/Zotero/storage/RZ2TXCHS/Lamport - 1978 - Time, clocks, and the ordering of events in a dist.pdf:application/pdf},
}
@article{osher_fronts_1988,
title = {Fronts propagating with curvature-dependent speed: {Algorithms} based on {Hamilton}-{Jacobi} formulations},
volume = {79},
issn = {0021-9991},
shorttitle = {Fronts propagating with curvature-dependent speed},
url = {https://www.sciencedirect.com/science/article/pii/0021999188900022},
doi = {10.1016/0021-9991(88)90002-2},
abstract = {We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand sides, by using techniques from hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be also used for more general Hamilton-Jacobi-type problems. We demonstrate our algorithms by computing the solution to a variety of surface motion problems.},
language = {en},
number = {1},
urldate = {2021-07-07},
journal = {Journal of Computational Physics},
author = {Osher, Stanley and Sethian, James A},
month = nov,
year = {1988},
pages = {12--49},
file = {ScienceDirect Snapshot:/Users/jack.hale/Zotero/storage/5S83WAEV/0021999188900022.html:text/html},
}
@article{hughes_isogeometric_2005,
title = {Isogeometric analysis: {CAD}, finite elements, {NURBS}, exact geometry and mesh refinement},
volume = {194},
issn = {0045-7825},
shorttitle = {Isogeometric analysis},
url = {https://www.sciencedirect.com/science/article/pii/S0045782504005171},
doi = {10.1016/j.cma.2004.10.008},
abstract = {The concept of isogeometric analysis is proposed. Basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model. For purposes of analysis, the basis is refined and/or its order elevated without changing the geometry or its parameterization. Analogues of finite element h- and p-refinement schemes are presented and a new, more efficient, higher-order concept, k-refinement, is introduced. Refinements are easily implemented and exact geometry is maintained at all levels without the necessity of subsequent communication with a CAD (Computer Aided Design) description. In the context of structural mechanics, it is established that the basis functions are complete with respect to affine transformations, meaning that all rigid body motions and constant strain states are exactly represented. Standard patch tests are likewise satisfied. Numerical examples exhibit optimal rates of convergence for linear elasticity problems and convergence to thin elastic shell solutions. A k-refinement strategy is shown to converge toward monotone solutions for advection–diffusion processes with sharp internal and boundary layers, a very surprising result. It is argued that isogeometric analysis is a viable alternative to standard, polynomial-based, finite element analysis and possesses several advantages.},
language = {en},
number = {39},
urldate = {2021-07-07},
journal = {Computer Methods in Applied Mechanics and Engineering},
author = {Hughes, T. J. R. and Cottrell, J. A. and Bazilevs, Y.},
month = oct,
year = {2005},
keywords = {-refinement, Boundary layers, CAD, Convergence, Finite element analysis, Fluid dynamics, Geometry, Internal layers, Mesh refinement, NURBS, Shells, Structural analysis},
pages = {4135--4195},
file = {ScienceDirect Snapshot:/Users/jack.hale/Zotero/storage/WSAUX82L/S0045782504005171.html:text/html;Submitted Version:/Users/jack.hale/Zotero/storage/35AYX58H/Hughes et al. - 2005 - Isogeometric analysis CAD, finite elements, NURBS.pdf:application/pdf},
}
@article{halton_retrospective_1970,
title = {A {Retrospective} and {Prospective} {Survey} of the {Monte} {Carlo} {Method}},
volume = {12},
issn = {0036-1445},
url = {https://epubs.siam.org/doi/abs/10.1137/1012001},
doi = {10.1137/1012001},
number = {1},
urldate = {2021-07-07},
journal = {SIAM Review},
author = {Halton, John H.},
month = jan,
year = {1970},
note = {Publisher: Society for Industrial and Applied Mathematics},
pages = {1--63},
file = {Submitted Version:/Users/jack.hale/Zotero/storage/MW28M9JK/Halton - 1970 - A Retrospective and Prospective Survey of the Mont.pdf:application/pdf},
}
@article{held_dynamic_1962,
title = {A {Dynamic} {Programming} {Approach} to {Sequencing} {Problems}},
volume = {10},
issn = {0368-4245},
url = {https://www.jstor.org/stable/2098806},
number = {1},
urldate = {2021-07-07},
journal = {Journal of the Society for Industrial and Applied Mathematics},
author = {Held, Michael and Karp, Richard M.},
year = {1962},
note = {Publisher: Society for Industrial and Applied Mathematics},
pages = {196--210},
}
@article{dijkstra_note_1959,
title = {A note on two problems in connexion with graphs},
volume = {1},
issn = {0029-599X, 0945-3245},
url = {http://link.springer.com/10.1007/BF01386390},
doi = {10.1007/BF01386390},
language = {en},
number = {1},
urldate = {2021-07-07},
journal = {Numerische Mathematik},
author = {Dijkstra, E. W.},
month = dec,
year = {1959},
pages = {269--271},
file = {Submitted Version:/Users/jack.hale/Zotero/storage/T3F3S76Y/Dijkstra - 1959 - A note on two problems in connexion with graphs.pdf:application/pdf},
}
@article{golub_calculating_1965,
title = {Calculating the {Singular} {Values} and {Pseudo}-{Inverse} of a {Matrix}},
volume = {2},
issn = {0887-459X},
url = {https://www.jstor.org/stable/2949777},
abstract = {A numerically stable and fairly fast scheme is described to compute the unitary matrices U and V which transform a given matrix A into a diagonal form Σ = U* AV, thus exhibiting A's singular values on Σ's diagonal. The scheme first transforms A to a bidiagonal matrix J, then diagonalizes J. The scheme described here is complicated but does not suffer from the computational difficulties which occasionally afflict some previously known methods. Some applications are mentioned, in particular the use of the pseudo-inverse AI = VΣIU* to solve least squares problems in a way which dampens spurious oscillation and cancellation.},
number = {2},
urldate = {2021-07-07},
journal = {Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis},
author = {Golub, G. and Kahan, W.},
year = {1965},
note = {Publisher: Society for Industrial and Applied Mathematics},
pages = {205--224},
}