- DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations
2022/12/28 by Kejun Tang, Xiaoliang Wan, Chao Yang · 26 citations
Decision Sciences · Engineering · Mathematics · Physics and Astronomy · #Adaptive sampling #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Collocation (remote sensing) #Computer science #Finite element method #Function (biology) #Machine learning #Mathematical analysis #Mathematical optimization #Mathematics #Method of mean weighted residuals #Model Reduction and Neural Networks #Monte Carlo method #Numerical methods in engineering #Partial differential equation #Probabilistic and Robust Engineering Design #Residual #Sampling (signal processing) #Set (abstract data type) #Statistics
- Weak-form collocation – A local meshless method in linear elasticity
2016/10/04 by Tiago da Silva Oliveira, T. Oliveira, A. Portela · 1 citation
Engineering · Mathematics · #Applied mathematics #Boundary element method #Collocation (remote sensing) #Collocation method #Computer science #Dam Engineering and Safety #Differential equation #Elasticity (physics) #Finite element method #Linear elasticity #Mathematical analysis #Mathematics #Meshfree methods #Numerical methods in engineering #Ordinary differential equation #Physics #Regularized meshless method #Rock Mechanics and Modeling #Singular boundary method
- An improved collocation method for multi-dimensional space–time variable-order fractional Schrödinger equations
2016/09/21 by A. H. Bhrawy, A.H. Bhrawy, M.A. Zaky +1 · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Collocation (remote sensing) #Collocation method #Differential equation #Fractional Differential Equations Solutions #Fractional calculus #Jacobi polynomials #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Numerical analysis #Numerical methods in engineering #Ordinary differential equation #Orthogonal polynomials #Space (punctuation) #Spectral method #Variable (mathematics)
- Influence of the Discretization Methods on the Distribution of Relaxation Times Deconvolution: Implementing Radial Basis Functions with DRTtools
2015/10/25 by Ting Hei Wan, Mattia Saccoccio, Chi Chen +1 · 34 citations
Chemical Engineering · Engineering · Mathematics · #Algorithm #Analytical Chemistry and Sensors #Applied mathematics #Artificial intelligence #Artificial neural network #Basis function #Collocation (remote sensing) #Computer science #Deconvolution #Discretization #Discretization error #Discretization of continuous features #Fuel Cells and Related Materials #Machine learning #Mathematical analysis #Mathematical optimization #Mathematics #Non-Destructive Testing Techniques #Piecewise #Radial basis function #Rate of convergence #Relaxation (psychology)
- A Radial Basis Function Partition of Unity Collocation Method for Convection–Diffusion Equations Arising in Financial Applications
2014/10/25 by Ali Safdari-Vaighani, Alfa Heryudono, Elisabeth Larsson · 1 citation
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Collocation (remote sensing) #Collocation method #Computer science #Convection–diffusion equation #Convergence (economics) #Differential Equations and Numerical Methods #Differential equation #Finite element method #Fractional Differential Equations Solutions #Mathematical analysis #Mathematical optimization #Mathematics #Numerical analysis #Ordinary differential equation #Partial differential equation #Partition of unity #Radial basis function
- A comparative study of the harmonic balance method and the orthogonal collocation method on stiff nonlinear systems
2014/02/21 by Sami Karkar, Bruno Cochelin, Christophe Vergez · 4 citations
Engineering · Mathematics · #Applied mathematics #Bladed Disk Vibration Dynamics #Collocation (remote sensing) #Collocation method #Computer science #Convergence (economics) #Differential equation #Dynamics and Control of Mechanical Systems #Engineering #Harmonic balance #Harmonics #Mathematical analysis #Mathematics #Nonlinear system #Physics #Piecewise #Vibration and Dynamic Analysis
- RBF Based Meshless Method for Large Scale Shallow Water Simulations: Experimental Validation
2010/01/01 by Y. Alhuri, Ahmed Naji, Driss Ouazar +1 · 1 citation
Engineering · Mathematics · #Numerical methods in engineering #Fluid Dynamics Simulations and Interactions #Geotechnical Engineering and Underground Structures #Collocation (remote sensing) #Computation #Grid #Scale (ratio) #Radial basis function #Regularized meshless method #Collocation method #Waves and shallow water #Mathematics #Applied mathematics #Singular boundary method #Mathematical optimization #Computer science #Mathematical analysis #Geology #Geometry #Algorithm #Engineering #Physics #Structural engineering #Differential equation #Remote sensing
- Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style
2009/09/01 by B. Boroomand, Soheil Soghrati, B. Movahedian · 1 citation
Engineering · Decision Sciences · Mathematics · #Numerical methods in engineering #Probabilistic and Robust Engineering Design #Electromagnetic Simulation and Numerical Methods #Mathematics #Collocation (remote sensing) #Applied mathematics #Boundary value problem #Transformation (genetics) #Regularized meshless method #Mathematical optimization #Partial differential equation #Series (stratigraphy) #Harmonic #Mathematical analysis #Singular boundary method #Computer science #Finite element method #Boundary element method
- A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
2009/08/13 by Z.J. Wang, Haiyang Gao · 23 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Collocation (remote sensing) #Computational Fluid Dynamics and Aerodynamics #Computer science #Conservation law #Discontinuous Galerkin method #Discretization #Extended finite element method #Finite element method #Fluid Dynamics and Turbulent Flows #Galerkin method #Geometry #Grid #Hexahedron #Mathematical analysis #Mathematical optimization #Mathematics #Penalty method #Physics #Quadrilateral #Spectral element method #Spectral method
- Space–time meshfree collocation method: Methodology and application to initial‐boundary value problems
2009/05/28 by Hennadiy Netuzhylov, Andreas Zilian · 1 citation
Engineering · Mathematics · #Numerical methods in engineering #Geotechnical Engineering and Underground Structures #Fluid Dynamics Simulations and Interactions #Kronecker delta #Meshfree methods #Discretization #Mathematics #Interpolation (computer graphics) #Collocation (remote sensing) #Regularized meshless method #Partial differential equation #Boundary value problem #Applied mathematics #Kernel (algebra) #Collocation method #Ordinary differential equation #Moving least squares #Mathematical optimization #Singular boundary method #Computer science #Finite element method #Mathematical analysis #Differential equation #Boundary element method #Discrete mathematics
- Meshfree and particle methods and their applications
2002/01/01 by Shaofan Li, Wing Kam Liu · 14 citations
Engineering · Mathematics · #Boundary value problem #Classical mechanics #Collocation (remote sensing) #Compressibility #Computer science #Engineering #Finite element method #Fluid Dynamics Simulations and Interactions #Galerkin method #Geology #Geotechnical Engineering and Underground Structures #Kernel (algebra) #Mathematical analysis #Mathematics #Mechanics #Meshfree methods #Numerical methods in engineering #Particle (ecology) #Particle method #Physics #Smoothed-particle hydrodynamics #Structural engineering
- A spectral element method for fluid dynamics: Laminar flow in a channel expansion
1984/06/01 by Anthony T Patera, Anthony T. Patera · 60 citations
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Collocation (remote sensing) #Computational Fluid Dynamics and Aerodynamics #Computer science #Discretization #Finite element method #Fluid Dynamics and Turbulent Flows #Geometry #Laminar flow #Mathematical analysis #Mathematics #Mechanics #Mixed finite element method #Physics #Pressure-correction method #Projection method #Spectral element method #Spectral method