Journal of Computational Physics, ISSN 0021-9991, 12/2019, Volume 398, p. 108892

•We investigate the isogeometric analysis based on extended Loop subdivision approach for solving surface PDEs.•The performance is evaluated by solving various...

Isogeometric analysis | Extended Loop subdivision | Surface PDEs | POLYNOMIAL SPLINES | GEOMETRIC DESIGN | IMPLEMENTATION | CATMULL-CLARK SUBDIVISION | PHYSICS, MATHEMATICAL | NURBS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CAD BOUNDARY | PARAMETERIZATION | COMPUTATIONAL DOMAIN | DIFFUSION | FINITE-ELEMENT-METHOD | Accuracy | Solution space | Basis functions | Splines | Dependent variables | Mathematics - Numerical Analysis

Isogeometric analysis | Extended Loop subdivision | Surface PDEs | POLYNOMIAL SPLINES | GEOMETRIC DESIGN | IMPLEMENTATION | CATMULL-CLARK SUBDIVISION | PHYSICS, MATHEMATICAL | NURBS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CAD BOUNDARY | PARAMETERIZATION | COMPUTATIONAL DOMAIN | DIFFUSION | FINITE-ELEMENT-METHOD | Accuracy | Solution space | Basis functions | Splines | Dependent variables | Mathematics - Numerical Analysis

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2017, Volume 323, pp. 1 - 15

Past work on integration methods that preserve a conformal symplectic structure focuses on Hamiltonian systems with weak linear damping. In this work, systems...

Structure-preserving algorithm | Multi-symplectic PDE | Conformal symplectic | BIRKHOFFIAN SYSTEMS | NUMERICAL-METHODS | MATHEMATICS, APPLIED | FINITE-DIFFERENCE SCHEMES | VARIATIONAL INTEGRATORS | TIME-STEPPING ALGORITHMS | NONLINEAR DYNAMICS | CONSERVATION | STRUCTURE-PRESERVING ALGORITHMS | GEOMETRIC INTEGRATION | HAMILTONIAN WAVE-EQUATIONS | Analysis | Numerical analysis | Algorithms | Environmental law

Structure-preserving algorithm | Multi-symplectic PDE | Conformal symplectic | BIRKHOFFIAN SYSTEMS | NUMERICAL-METHODS | MATHEMATICS, APPLIED | FINITE-DIFFERENCE SCHEMES | VARIATIONAL INTEGRATORS | TIME-STEPPING ALGORITHMS | NONLINEAR DYNAMICS | CONSERVATION | STRUCTURE-PRESERVING ALGORITHMS | GEOMETRIC INTEGRATION | HAMILTONIAN WAVE-EQUATIONS | Analysis | Numerical analysis | Algorithms | Environmental law

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 344, Issue 2, pp. 655 - 666

The determination of solutions of the Jacobi partial differential equations (PDEs) for finite-dimensional Poisson systems is considered. In particular, a novel...

Poisson structures | Time reparametrizations | Hamiltonian systems | Jacobi partial differential equations | Finite-dimensional Poisson systems | Darboux canonical form | GEOMETRIC PHASES | MATHEMATICS, APPLIED | IDENTITIES | STABILITY | GLOBAL ANALYSIS | CLASSIFICATION | HAMILTONIAN-STRUCTURE | MATHEMATICS | time reparametrizations | DYNAMICAL-SYSTEMS | INVARIANT TORI | CONSTRUCTION | LOTKA-VOLTERRA EQUATIONS | finite-dimensional Poisson systems

Poisson structures | Time reparametrizations | Hamiltonian systems | Jacobi partial differential equations | Finite-dimensional Poisson systems | Darboux canonical form | GEOMETRIC PHASES | MATHEMATICS, APPLIED | IDENTITIES | STABILITY | GLOBAL ANALYSIS | CLASSIFICATION | HAMILTONIAN-STRUCTURE | MATHEMATICS | time reparametrizations | DYNAMICAL-SYSTEMS | INVARIANT TORI | CONSTRUCTION | LOTKA-VOLTERRA EQUATIONS | finite-dimensional Poisson systems

Journal Article

Computer Graphics Forum, ISSN 0167-7055, 12/2015, Volume 34, Issue 8, pp. 104 - 118

In this paper, we deal with the problem of computing the distance to a surface (a curve in two dimensional) and consider several distance function...

variational methods | I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms | iterative optimization | and systems; G.1.8 [Numerical Analysis]: Partial Differential Equations—Iterative solution techniques | distance function approximations | languages | INTERPOLATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALGORITHM | EQUATION | Studies | Partial differential equations | Analysis | Computer graphics | Approximations | Approximation | Computation | Mathematical analysis | Mathematical models | Two dimensional

variational methods | I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms | iterative optimization | and systems; G.1.8 [Numerical Analysis]: Partial Differential Equations—Iterative solution techniques | distance function approximations | languages | INTERPOLATION | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ALGORITHM | EQUATION | Studies | Partial differential equations | Analysis | Computer graphics | Approximations | Approximation | Computation | Mathematical analysis | Mathematical models | Two dimensional

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2019, Volume 394, Issue C, pp. 658 - 678

Microscopic (pore-scale) properties of porous media affect and often determine their macroscopic (continuum- or Darcy-scale) counterparts. Understanding the...

Bayesian Networks | Porous media | Global sensitivity analysis | Mutual Information | Causality | Energy storage | INFORMATION | DIVERGENCES | PHYSICS, MATHEMATICAL | GLOBAL SENSITIVITY-ANALYSIS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MEASURING UNCERTAINTY IMPORTANCE | ENTROPY | Correlation | Uncertainty | Sensitivity analysis | Transport phenomena | Statistical analysis | Workflow | Macroscopic models | Probability density functions | Design engineering | Bayesian analysis | Geometric constraints | Material properties

Bayesian Networks | Porous media | Global sensitivity analysis | Mutual Information | Causality | Energy storage | INFORMATION | DIVERGENCES | PHYSICS, MATHEMATICAL | GLOBAL SENSITIVITY-ANALYSIS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MEASURING UNCERTAINTY IMPORTANCE | ENTROPY | Correlation | Uncertainty | Sensitivity analysis | Transport phenomena | Statistical analysis | Workflow | Macroscopic models | Probability density functions | Design engineering | Bayesian analysis | Geometric constraints | Material properties

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 8/2011, Volume 21, Issue 4, pp. 1322 - 1364

We consider the probabilistic numerical scheme for fully nonlinear partial differential equations suggested in [Comm. Pure Appl. Math. 60 (2007) 1081–1110] and...

Viscosity | Approximation | Geometric growth | Differential equations | Nonlinearity | Numerical schemes | Random variables | Diffusion coefficient | Curvature | Monotone schemes | Second order backward stochastic differential equations | Monte Carlo approximation | Viscosity solutions | JACOBI-BELLMAN EQUATIONS | STOCHASTIC DIFFERENTIAL-EQUATIONS | VOLATILITY MODELS | second order backward stochastic differential equations | STATISTICS & PROBABILITY | SIMULATION | OPTIONS | CONSISTENCY | MONOTONE-APPROXIMATION SCHEMES | COEFFICIENTS | CONVERGENCE | ERROR-BOUNDS | monotone schemes | 65C05 | 49L25

Viscosity | Approximation | Geometric growth | Differential equations | Nonlinearity | Numerical schemes | Random variables | Diffusion coefficient | Curvature | Monotone schemes | Second order backward stochastic differential equations | Monte Carlo approximation | Viscosity solutions | JACOBI-BELLMAN EQUATIONS | STOCHASTIC DIFFERENTIAL-EQUATIONS | VOLATILITY MODELS | second order backward stochastic differential equations | STATISTICS & PROBABILITY | SIMULATION | OPTIONS | CONSISTENCY | MONOTONE-APPROXIMATION SCHEMES | COEFFICIENTS | CONVERGENCE | ERROR-BOUNDS | monotone schemes | 65C05 | 49L25

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2019, Volume 361, pp. 766 - 776

Bicubic B-spline surface constrained by the Biharmonic PDE is presented in this paper. By representing the Biharmonic PDE in the form of the bilinear B-spline...

Biharmonic PDE | Geometric computing | Surface generation | Cubic B-spline | Bicubic B-spline surface | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | BEZIER SURFACES | PARTIAL-DIFFERENTIAL-EQUATIONS | GENERATE

Biharmonic PDE | Geometric computing | Surface generation | Cubic B-spline | Bicubic B-spline surface | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | BEZIER SURFACES | PARTIAL-DIFFERENTIAL-EQUATIONS | GENERATE

Journal Article

2016, Lecture Notes in Mathematics, ISBN 9783319423081, Volume 2161

eBook

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 12/2012, Volume 13, Issue 6, pp. 2491 - 2529

We generalize our geometric theory on extended crystal PDEs and their stability, to the category QS of quantum supermanifolds. By using the algebraic topologic...

Conservation laws | Integral bordisms in quantum super PDEs | (Un)stable quantum extended crystal super PDEs | Quantum (super)gravity | (Un)stable quantum solutions | Quantum singular super PDEs | Existence of local and global solutions in quantum super PDEs | (Un)stable quantum super PDEs | MATHEMATICS, APPLIED | MHD-PDES | STABILITY | BOUNDARY-VALUE-PROBLEMS | INTEGRAL-BORDISM-GROUPS | FINITE IRREDUCIBLE SUBGROUPS | BROKEN SYMMETRIES | GEOMETRIC APPROACH | PARTIAL-DIFFERENTIAL-EQUATIONS | (CO)BORDISM GROUPS | GENERALIZED DALEMBERT EQUATION | Dynamic tests | Stability | Partial differential equations | Mathematical analysis | Crystals | Plasmas | Dynamical systems | Nuclides

Conservation laws | Integral bordisms in quantum super PDEs | (Un)stable quantum extended crystal super PDEs | Quantum (super)gravity | (Un)stable quantum solutions | Quantum singular super PDEs | Existence of local and global solutions in quantum super PDEs | (Un)stable quantum super PDEs | MATHEMATICS, APPLIED | MHD-PDES | STABILITY | BOUNDARY-VALUE-PROBLEMS | INTEGRAL-BORDISM-GROUPS | FINITE IRREDUCIBLE SUBGROUPS | BROKEN SYMMETRIES | GEOMETRIC APPROACH | PARTIAL-DIFFERENTIAL-EQUATIONS | (CO)BORDISM GROUPS | GENERALIZED DALEMBERT EQUATION | Dynamic tests | Stability | Partial differential equations | Mathematical analysis | Crystals | Plasmas | Dynamical systems | Nuclides

Journal Article

2016, Springer Proceedings in Mathematics & Statistics, ISBN 9783319415369, Volume 176, 290

This book collects recent research papers by respected specialists in the field. It presents advances in the field of geometric properties for parabolic and...

Discrete groups | Mathematics | Ordinary Differential Equations | Functional Analysis | Calculus of Variations and Optimal Control; Optimization | Convex and Discrete Geometry | Partial Differential Equations

Discrete groups | Mathematics | Ordinary Differential Equations | Functional Analysis | Calculus of Variations and Optimal Control; Optimization | Convex and Discrete Geometry | Partial Differential Equations

eBook

2012, Graduate studies in mathematics, ISBN 0821872915, Volume 133, xix, 363

Book

Journal of Computational Physics, ISSN 0021-9991, 03/2017, Volume 332, p. 257

RBF-generated finite differences (RBF-FD) have in the last decade emerged as a very powerful and flexible numerical approach for solving a wide range of PDEs....

Geometry | Interpolation | Splines | Circuits | Topography | Harmonic analysis | Polynomials | Finite element analysis | Elliptic functions | Geometric accuracy | Multivariate analysis

Geometry | Interpolation | Splines | Circuits | Topography | Harmonic analysis | Polynomials | Finite element analysis | Elliptic functions | Geometric accuracy | Multivariate analysis

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 08/2018, Volume 338, p. 440

Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of...

Geometry | Maps | Approximation | Partial differential equations | Computer aided design--CAD | Mathematical analysis | Spectral element method | Software | Spectra | Galerkin method | Geometric accuracy | Meshing

Geometry | Maps | Approximation | Partial differential equations | Computer aided design--CAD | Mathematical analysis | Spectral element method | Software | Spectra | Galerkin method | Geometric accuracy | Meshing

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 02/2018, Volume 173, Issue 1-2, pp. 1 - 45

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected...

Minimal matching | Optimal transport | Geometric probability | TRANSPORTATION COST | CONVERGENCE | STATISTICS & PROBABILITY | CURVATURE-DIMENSION CONDITION | Matching | Asymptotic series | Monge-Ampere equation | Random variables | Asymptotic methods | Independent variables

Minimal matching | Optimal transport | Geometric probability | TRANSPORTATION COST | CONVERGENCE | STATISTICS & PROBABILITY | CURVATURE-DIMENSION CONDITION | Matching | Asymptotic series | Monge-Ampere equation | Random variables | Asymptotic methods | Independent variables

Journal Article

Communications in Computational Physics, ISSN 1815-2406, 05/2016, Volume 19, Issue 5, pp. 1375 - 1396

This paper explores the discrete singular convolution method for Hamiltonian PDEs. The differential matrices corresponding to two delta type kernels of the...

differential matrix | Discrete singular convolution | symplectic integrator | Hamiltonian PDEs | GEOMETRIC INTEGRATORS | PHYSICS, MATHEMATICAL | EQUATION | WAVE-PROPAGATION | SCHEMES

differential matrix | Discrete singular convolution | symplectic integrator | Hamiltonian PDEs | GEOMETRIC INTEGRATORS | PHYSICS, MATHEMATICAL | EQUATION | WAVE-PROPAGATION | SCHEMES

Journal Article

1996, ISBN 9789810225209, x, 747

Book

2005, Contemporary mathematics, ISBN 9780821833865, Volume 368., viii, 414

Book

International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 10/2014, Volume 11, Issue 9, pp. 1460039 - 1-1460039-35

Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the...

Partial differential equations | Wave/particle duality | Characteristics | Hamilton-Jacobi theory | Bicharacteristics | Geometric singularities of solutions | Jet spaces | characteristics | bicharacteristics | FIELD-THEORIES | PHYSICS, MATHEMATICAL | NONLINEAR DIFFERENTIAL-EQUATIONS | MULTIVALUED SOLUTIONS | MECHANICS | HIGHER-ORDER | wave/particle duality | jet spaces | geometric singularities of solutions | Singularities | Mathematical analysis | Quantum mechanics | Workshops | Well posed problems | Invariants | Cauchy problem

Partial differential equations | Wave/particle duality | Characteristics | Hamilton-Jacobi theory | Bicharacteristics | Geometric singularities of solutions | Jet spaces | characteristics | bicharacteristics | FIELD-THEORIES | PHYSICS, MATHEMATICAL | NONLINEAR DIFFERENTIAL-EQUATIONS | MULTIVALUED SOLUTIONS | MECHANICS | HIGHER-ORDER | wave/particle duality | jet spaces | geometric singularities of solutions | Singularities | Mathematical analysis | Quantum mechanics | Workshops | Well posed problems | Invariants | Cauchy problem

Journal Article

Mathematics of Control, Signals, and Systems, ISSN 0932-4194, 03/2014, Volume 26, Issue 1, pp. 1 - 46

We study the exact controllability, by a reduced number of controls, of coupled cascade systems of PDE's and the existence of exact insensitizing controls for...

Geometric conditions | HUM | Locally distributed observability | Schrödinger equations | Locally distributed control | Cascade systems | Parabolic systems | Abstract linear evolution equations | Insensitizing controls | Boundary observability | Boundary control | Indirect controllability | Optimal conditions | Hyperbolic systems | EXISTENCE | PARABOLIC-SYSTEM | COST | NULL-CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | SEMILINEAR HEAT-EQUATION | STABILIZATION | ENGINEERING, ELECTRICAL & ELECTRONIC | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equations | ONE CONTROL FORCE | TRANSMUTATION | INDIRECT BOUNDARY OBSERVABILITY | Mathematical analysis | Control systems | Mathematics - Optimization and Control

Geometric conditions | HUM | Locally distributed observability | Schrödinger equations | Locally distributed control | Cascade systems | Parabolic systems | Abstract linear evolution equations | Insensitizing controls | Boundary observability | Boundary control | Indirect controllability | Optimal conditions | Hyperbolic systems | EXISTENCE | PARABOLIC-SYSTEM | COST | NULL-CONTROLLABILITY | AUTOMATION & CONTROL SYSTEMS | SEMILINEAR HEAT-EQUATION | STABILIZATION | ENGINEERING, ELECTRICAL & ELECTRONIC | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Schrodinger equations | ONE CONTROL FORCE | TRANSMUTATION | INDIRECT BOUNDARY OBSERVABILITY | Mathematical analysis | Control systems | Mathematics - Optimization and Control

Journal Article

Milan Journal of Mathematics, ISSN 1424-9286, 12/2012, Volume 80, Issue 2, pp. 469 - 501

Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving...

65M15 | Secondary 35K99 | Surface finite elements | Mathematics | advection diffusion equation | 76R99 | Analysis | Mathematics, general | Primary 65M60 | 35R01 | ALE | 35R37 | interface motion | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | GRAIN-BOUNDARY MOTION | DIFFUSE INTERFACE APPROACH | GEOMETRIC EVOLUTION-EQUATIONS | ELLIPTIC-EQUATIONS | FINITE-ELEMENT-METHOD | NUMERICAL-SIMULATION | PHASE-FIELD MODEL | CLOSEST POINT METHOD | Differential equations | Beer

65M15 | Secondary 35K99 | Surface finite elements | Mathematics | advection diffusion equation | 76R99 | Analysis | Mathematics, general | Primary 65M60 | 35R01 | ALE | 35R37 | interface motion | MATHEMATICS, APPLIED | PARABOLIC EQUATIONS | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | GRAIN-BOUNDARY MOTION | DIFFUSE INTERFACE APPROACH | GEOMETRIC EVOLUTION-EQUATIONS | ELLIPTIC-EQUATIONS | FINITE-ELEMENT-METHOD | NUMERICAL-SIMULATION | PHASE-FIELD MODEL | CLOSEST POINT METHOD | Differential equations | Beer

Journal Article

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