[PDF] Top 20 Adaptive numerical methods for PDEs

... specific numerical algorithm but rather have addressed the question of whether nonlinear or adaptive algorithms could possibly be of benefit in numerically approximating the solution of a ...an ... See full document

... for numerical solution of boundary-value problems in continuum ...order methods by which ac- curate results can be obtained using relatively coarse discretizations of the domain of ... See full document

... Vortex methods denotes a class of numerical methods for approximating the solution of the incompressible Navier Stokes or Euler equations (ν = ...a numerical procedure, solving succes- sively ... See full document

... pseudo-spectral methods, one typically uses a frequency cut-off to remove the fastest oscillations, while in the case of finite- difference-based methods the common recipe is to introduce a small amount of ... See full document

... mesh methods for solving one-dimensional problems in Q-tensor ...the adaptive grids provided the same level of accuracy as uniform grids, but using far fewer points, resulting in a computational ...coupled ... See full document

... designing adaptive iterative methods for solving operator ...some adaptive numerical methods for elliptic operator equations have been developed by using wavelet bases and ... See full document

... space–adaptive methods, which mostly employ explicit or semi–explicit time discretizations, is that the finest spatial grid size imposes a small time step in order to fulfill the stability criterion of the ... See full document

... Temperature profile of a nuclear fuel rod can be well defined using different numerical methods with appropriate boundary conditions. Antar [1] offered a simplified numerical solution of unsteady ... See full document

... several numerical simulations, which solve the CH equation under a wide range of initial ...presented numerical examples do not only corroborate the analytical results, but also demonstrate some of the ... See full document

... spectral methods are ideally suited for proper boundary conditions, as a boundary condition can be specified ...spectral methods test case solver will use a Fourier basis to avoid the boundary condition ... See full document

... collocation methods becomes large when the number of centers increases, while reducing the number of centers im- proves the conditioning [9, ...obtain numerical solution with the minimal numbers of centers, ... See full document

... the numerical solution of various types of PDEs, due to the flexibility with respect to geometry and high order of convergence ...meshless methods, the two major deficiencies are the computational ... See full document

... Dielectric breakdown in transformers is most frequently initiated by partial discharges. The consequences of these types of occurrences can be hazardous if not detected in a timely fashion. Regular PD analysis gives an ... See full document

... meshless methods, they have been extensively used in scattered data ...and adaptive wavelet method to solve the Perona-Malik equation in terms of locally shifted ...the numerical results are provided ... See full document

... multidimensional PDEs ob- tained in the recent years by the author and in collaborations, which have been presented at the Summer School CEMRACS-2013, “Modeling and simulation of complex systems: Stochastic and ... See full document

... In Figure 2 we show the time evolution of the time step for different initial CFL , i.e., for different initial time step sizes, using the finite volume scheme on a regular grid with global time adaptivity and the RKF 2(3) ... See full document

... In this section we describe the numerical approximation of the implicit sur- face φ-equations of Section 7. For computational purposes it is natural to seek to exploit these formulations by using a bulk ... See full document

... and numerical solutions of ODEs and PDEs based on MS and FD methods, respectively, are ...of PDEs are performed, determining steady-state, multi-degree-of-freedom, ... See full document

... mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential ...mesh methods designed for ... See full document

... of numerical methods for the time integration of semi-linear problems has been proposed by the application of the exponential ...(ETD) methods. Few years later, a modification of the ETD Runge- Kutta ... See full document