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Advanced materials research, ISSN 1022-6680, 08/2013, Volume 753-755, pp. 195 - 198
.... Therefore, the construction of polynomial chaos expansion with points of monomial cubature rules, which need fewer points than other kinds of integral, is particularly attractive in dealing with computational model for the forming simulation. An automobile threated plate is used to illustrate the validation of the method. 
Monomial cubature rules | Numerical simulation | Polynomial chaos expansion | Tolerance prediction | Upsetting-extruding process
Journal Article
SIAM journal on scientific computing, ISSN 1095-7197, 2005, Volume 27, Issue 3, pp. 1118 - 1139
Recently there has been a growing interest in designing efficient methods for the solution of ordinary/ partial differential equations with random inputs. To... 
Collocation methods | Uncertainty quantification | Stochastic inputs | Differential equations | MONOMIAL CUBATURE RULES | CHAOS | MATHEMATICS, APPLIED | uncertainty quantification | STROUD | STOCHASTIC FINITE-ELEMENTS | MODELING UNCERTAINTY | stochastic inputs | SIMULATIONS | collocation methods | differential equations
Journal Article
Journal of Complexity, ISSN 0885-064X, 04/2018, Volume 45, pp. 22 - 54
.... We use this result to show that, without any hypothesis on the support of μ, there is always a cubature rule for μ with at most 32d(d−1... 
Quadrature | Plane algebraic curves | Gauss quadrature | Cubature | Truncated moment problem | Szegő quadrature | MATHEMATICS, APPLIED | EXTENSIONS | STROUD | COMPILATION | TCHAKALOFFS THEOREM | MONOMIAL CUBATURE RULES | POLYNOMIALS | INTEGRALS | MATHEMATICS | Szego quadrature | FORMULAS
Journal Article
Journal of dynamic systems, measurement, and control, ISSN 1528-9028, 2018, Volume 140, Issue 3
.... The proposed cubature points can be used as an efficient alternative to the Gauss–Hermite (GH) and Gauss–Legendre quadrature rules, but with significantly fewer number... 
MONOMIAL CUBATURE RULES | INSTRUMENTS & INSTRUMENTATION | UNCERTAINTY PROPAGATION | SYMMETRIC PLANAR REGIONS | SPARSE GRIDS | POLYNOMIAL-CHAOS | TRACKING | NUMERICAL-INTEGRATION | COMPILATION | GAUSSIAN FILTERS | FORMULAS | AUTOMATION & CONTROL SYSTEMS
Journal Article
Journal of Guidance, Control, and Dynamics, ISSN 0731-5090, 2018, Volume 41, Issue 3, pp. 673 - 688
Uncertainty in aircraft trajectory planning and prediction generates major challenges for the future air traffic management system. Therefore, understanding... 
MONOMIAL CUBATURE RULES | CONFLICT-RESOLUTION | INSTRUMENTS & INSTRUMENTATION | OPTIMIZATION | ENGINEERING, AEROSPACE | STROUD | Wind | Uncertainty | Trajectory control | Traffic planning | Air traffic management | Environmental impact | Aircraft control | Traffic capacity | Trajectory planning | Optimal control | Traffic safety | Flight planning | Aircraft | Meteorology
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 2008, Volume 58, Issue 10, pp. 1515 - 1520
Numerical integration formulas in n-dimensional nonsymmetric Euclidean space of degree two, consisting of n + 1 equally weighted points, are discussed, for a... 
Cubature formulas | Numerical integration | MONOMIAL CUBATURE RULES | MATHEMATICS, APPLIED | COMPILATION | numerical integration | cubature formulas | STROUD
Journal Article
Journal of Economic Dynamics and Control, ISSN 0165-1889, 2011, Volume 35, Issue 2, pp. 240 - 251
Journal Article
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2007, Volume 45, Issue 1, pp. 193 - 205
Journal Article
Computers and Structures, ISSN 0045-7949, 2008, Volume 86, Issue 23, pp. 2102 - 2108
.... Therefore, the construction of polynomial chaos expansion with points of monomial cubature rules is particularly attractive in dealing with large computational model... 
Uncertainty quantification | Monomial cubature rules | Sampling points | Polynomial chaos expansion | STROUD | COMPILATION | METHODOLOGY | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, CIVIL | MODELING UNCERTAINTY | FORMULAS | PROPAGATION | BIOLOGICAL-SYSTEMS
Journal Article
Optics express, ISSN 1094-4087, 2013, Volume 21, Issue 1, pp. 87 - 101
We demonstrate how a tightly-focused coherent TEMmn laser beam can be computed in the finite-difference time-domain (FDTD) method. The electromagnetic field... 
MONOMIAL CUBATURE RULES | IMAGE FIELD | OPTICAL SYSTEMS | STROUD | ELECTROMAGNETIC DIFFRACTION | COMPILATION | MEDIA | OPTICS
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2002, Volume 149, Issue 1, pp. 1 - 12
This paper gives a personal bird's eye view of some aspects of multivariate numerical integration. It will sketch what happened during the past 50 years and... 
Quadrature | Cubature | Numerical integration | cubature | MONOMIAL CUBATURE RULES | MATHEMATICS, APPLIED | quadrature | numerical integration | STROUD | COMPILATION | FORMULAS
Journal Article
Journal of Magnetism and Magnetic Materials, ISSN 0304-8853, 08/2016, Volume 412, pp. 132 - 137
Journal Article
Journal of Magnetism and Magnetic Materials, ISSN 0304-8853, 05/2015, Volume 381, pp. 440 - 445
In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the... 
MONOMIAL CUBATURE RULES | PHYSICS, CONDENSED MATTER | COMPILATION | PRISMS | STROUD | MATERIALS SCIENCE, MULTIDISCIPLINARY | Magnetization | Analysis | Accuracy | Tensors | Numerical integration | Computation | Mathematical analysis | Exact solutions | Mathematical models | Demagnetizing
Journal Article
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 03/2008, Volume 56, Issue 7, pp. 899 - 925
.... Both the area and boundary integrals are evaluated using order 2N Gauss cubature rules. The use of exact integration for the area integrals leads naturally to a full mass matrix... 
penalty method | spectral element | finite volume | finite element | Lagrange | Fekete | Finite volume | Penalty method | Spectral element | Finite element | MESHES | STROUD | PHYSICS, FLUIDS & PLASMAS | SPHERE | EQUATIONS | COMPILATION | FLOW | FINITE-VOLUME | MONOMIAL CUBATURE RULES | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SPECTRAL ELEMENT METHOD | EQUATORIAL SOLITARY WAVES
Journal Article
International Journal for Numerical Methods in Fluids, ISSN 0271-2091, 07/2010, Volume 63, Issue 9, pp. 1077 - 1102
Journal Article