A5036702793- Numerical methods in engineering
- Advanced Numerical Methods in Computational Mathematics
- Electromagnetic Simulation and Numerical Methods
- Model Reduction and Neural Networks
- Fractional Differential Equations Solutions
- Numerical methods for differential equations
- Differential Equations and Numerical Methods
- Composite Structure Analysis and Optimization
- Nonlinear Waves and Solitons
- Additive Manufacturing Materials and Processes
- Advanced Numerical Analysis Techniques
- Additive Manufacturing and 3D Printing Technologies
- Ocular Surface and Contact Lens
- Advanced Mathematical Modeling in Engineering
- Electromagnetic Scattering and Analysis
- Fluid Dynamics and Turbulent Flows
- Manufacturing Process and Optimization
- Stochastic processes and financial applications
- Probabilistic and Robust Engineering Design
- Vibration and Dynamic Analysis
- Non-Destructive Testing Techniques
- Numerical Methods and Algorithms
- Industrial Vision Systems and Defect Detection
- Fluid Dynamics and Vibration Analysis
- Housing Market and Economics
University of Massachusetts Dartmouth
2014-2024
Uppsala University
2016
Informa (Sweden)
2016
University of Delaware
2007-2011
Radial basis function (RBF) approximation has the potential to provide spectrally accurate approximations for data given at scattered node locations. For smooth solutions, best accuracy a number of points is typically achieved when functions are scaled be nearly flat. This also results in linearly dependent and severe ill-conditioning interpolation matrices. Fornberg, Larsson, Flyer recently generalized RBF-QR method numerically stable approach with flat Gaussian RBFs arbitrary sets up three...
Recently, collocation-based radial basis function (RBF) partition of unity methods (PUMs) for solving partial differential equations have been formulated and investigated numerically theoretically. When combined with stable evaluation such as the RBF-QR method, high order convergence rates can be achieved sustained under refinement. However, some numerical issues remain. The method is sensitive to node layout, condition numbers increase refinement level. Here, we propose a modified...
We consider model problems for the tear film over multiple blink cycles that utilize a single equation film; non-linear partial differential governs thickness arises from lubrication theory. The two models we arise considering absence of naturally occurring surfactant and case when is strongly affecting surface tension. considered on time-varying domain length with specified volume flux at each end; only one end moving, which analogous to upper eyelid moving blink. Realistic lid motion...
Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 6 March 2020Accepted: 08 February 2021Published online: 26 April 2021Keywordsradial basis function, least squares, partial differential equation, elliptic problem, Neumann condition, RBF-FDAMS Subject Headings65N06, 65N12, 65N35Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3
Meshfree methods based on radial basis function (RBF) approximation are of interest for numerical solution partial differential equations because they flexible with respect to the geometry computational domain, can provide high order convergence, not more complicated problems many space dimensions and allow local refinement. The aim this paper is show that Rosenau equation, as an example initial-boundary value problem multiple boundary conditions, be implemented using RBF methods. We extend...
Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were proposed and analyzed [8]. These specially use reduced precision the implicit computations full explicit computations. We develop a FORTRAN code to solve nonlinear system of ordinary differential equations using mixed additive (MP-ARK) on IBM POWER9 Intel x86_64 chips. The convergence, accuracy, runtime, energy consumption these is explored. show that MP-ARK efficiently produce...
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when high level theory the electronic structure is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with partition unity approach. node refinement allows to greatly reduce number sample points by employing local error estimate. and its scaling behavior evaluated model function in 2, 3 4 dimensions. developed more rapid reliable surface...
Abstract The use of robust multiresponse constrained optimization techniques in which multiple-objective responses are involved is becoming a crucial part additive manufacturing (AM) processes. Common and popular techniques, most cases, rely on the assumption independent responses. In practice, however, many desired quality characteristics can be correlated. this work, we propose technique based three ingredients: hybrid self-organizing (HSO) method, desirability function (DF), evolutionary...
This paper develops two local mesh-free methods for designing stencil weights and spatial discretization, respectively, parabolic partial differential equations (PDEs) of convection–diffusion–reaction type. These are known as the radial-basis-function generated finite-difference method Hermite method. The convergence stability these schemes investigated numerically using some examples in three dimensions with regularly irregularly shaped domains. Then we consider numerical pricing European...