Journal of Computational Physics
Space-time finite element methods for second-order hyperbolic equations
Computer Methods in Applied Mechanics and Engineering
Computer Methods in Applied Mechanics and Engineering
Space-time spectral element methods for one-dimensional nonlinear advection-diffusion problems
Journal of Computational Physics
Journal of Computational Physics
Time finite element methods for initial value problems
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998)
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
Computation of Periodic Solution Bifurcations in ODEs Using Bordered Systems
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Concepts and Applications of Finite Element Analysis
Concepts and Applications of Finite Element Analysis
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Adjoint sensitivities of time-periodic nonlinear structural dynamics via model reduction
Computers and Structures
Structural and Multidisciplinary Optimization
Hi-index | 31.45 |
In this paper, the spectral element (SE) method is applied in time to find the entire time-periodic or transient solution of time-dependent differential equations. The time-periodic solution is computed by enforcing periodicity of the element set. Of particular interest are periodic forcing functions possessing high frequency content. To maintain the spectral accuracy for such forcing functions, an h-refinement scheme is employed near the semi-discontinuity without increasing the number of degrees of freedom. Time discretization by spectral elements is applied initially to a standard form of a set of linear, first-order differential equations subject to harmonic excitation and an excitation admitting rapid variation. Other case studies include the application of the SE approach to parabolic and hyperbolic partial differential equations. The first-order form of these equations is obtained through semi-discretization using conventional finite-element, spectral element and finite-difference schemes. Element clustering (h-refinement) is applied to maintain the high accuracy and efficiency in the region of the forcing function admitting rapid variation. The convergence in time of the method is demonstrated. In some cases, machine precision is obtained with 25 degrees of freedom per cycle. Finally the method is applied to a weakly nonlinear problem with time-periodic solution to demonstrate its future applicability to the analysis of limit-cycle oscillations in aeroelastic systems.