A Krylov-Subspace-Based Exponential Time Integration Scheme for Discontinuous Galerkin Time-Domain Methods

2019 ◽  
Vol 55 (6) ◽  
pp. 1-5
Author(s):  
Jiawei Wang ◽  
Feng Chen ◽  
Xikui Ma ◽  
JingHui Shao ◽  
Zhen Kang ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Time Domain ◽  
Krylov Subspace ◽  
Time Integration ◽  
Integration Scheme ◽  
Exponential Time ◽  
Time Integration Scheme ◽  
Exponential Time Integration

scholarly journals Exponential Time Integration and Second-Order Difference Scheme for a Generalized Black-Scholes Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Zhongdi Cen ◽  
Anbo Le ◽  
Aimin Xu
Keyword(s):  
Difference Scheme ◽  
Time Integration ◽  
Second Order ◽  
Integration Scheme ◽  
Uniform Mesh ◽  
Central Difference ◽  
Exponential Time ◽  
Black Scholes ◽  
Time Integration Scheme ◽  
Exponential Time Integration

We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black-Scholes equation. We show that the scheme is second-order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.

Fast Exponential Time Integration for Pricing Options in Stochastic Volatility Jump Diffusion Models

2014 ◽  
Vol 4 (1) ◽  
pp. 52-68 ◽  
Author(s):  
Hong-Kui Pang ◽  
Hai-Wei Sun
Keyword(s):  
Stochastic Volatility ◽  
Temporal Integration ◽  
Time Integration ◽  
Computational Cost ◽  
Jump Diffusion ◽  
Integration Scheme ◽  
Arnoldi Method ◽  
Exponential Time ◽  
Jump Diffusion Model ◽  
Exponential Time Integration

AbstractThe stochastic volatility jump diffusion model with jumps in both return and volatility leads to a two-dimensional partial integro-differential equation (PIDE). We exploit a fast exponential time integration scheme to solve this PIDE. After spatial discretization and temporal integration, the solution of the PIDE can be formulated as the action of an exponential of a block Toeplitz matrix on a vector. The shift-invert Arnoldi method is employed to approximate this product. To reduce the computational cost, matrix splitting is combined with the multigrid method to deal with the shift-invert matrix-vector product in each inner iteration. Numerical results show that our proposed scheme is more robust and efficient than the existing high accurate implicit-explicit Euler-based extrapolation scheme.

Explicit Time Integration Algorithm for Fully Flexible Cell Molecular Dynamics

2006 ◽  
Vol 326-328 ◽  
pp. 337-340 ◽  
Author(s):  
Shi Dong Park ◽  
Maeng Hyo Cho
Keyword(s):  
Molecular Dynamics ◽  
Real Time ◽  
Time Domain ◽  
Time Integration ◽  
Unit Cell ◽  
Material Behavior ◽  
Integration Scheme ◽  
Time Reversibility ◽  
Time Integration Scheme ◽  
Splitting Time

Fully flexible cell with Nose-Poincare method preserves Hamiltonian in structure, so the extended Hamiltonian is preserved in the real time domain. In the previous development of Nose- Poincare method for NVT, NPT, and NT ensemble unit cell simulations, implicit algorithm such as generalized leapfrog integration scheme was used. The formulation and numerical implementatio n of the implicit formula is much more complicated because it includes nonlinear iteration procedur e. Furthermore, it is not easy to show time reversibility in implicit formula. Thus for these reasons, it is necessary to develop explicit formula in MD unit cell simulation. We develop fully flexible explicit Nσ T ensemble MD simulation algorithm. It guarantees the preservation of extended Hamil tonian in real time domain and time reversibility. The numerical implementation is easy and relative ly simple since it does not require iteration process. It is established by using the splitting time integ ration. It separates flexible cell Hamiltonian into several terms corresponding to each Hamiltonian part, so the simple and completely explicit recursion formula was obtained. Unit cell tension, shear test for bulk material tension and shear tests are performed to demonstrate the validity and performance of the present explicit molecular dynamics scheme formulated through the spitting method. We compare the results of the explicit splitting time integration scheme with those of the implicit generalized leapfrog time integration scheme. The proposed explicit NT unit cell simulati on method should serve as a powerful tool in the prediction of the material behavior.

Design for a Hybrid Absorbing Element in the Time Domain Using PML and Infinite Element Concepts

2014 ◽  
Author(s):  
Jeffrey L. Cipolla
Keyword(s):  
Time Domain ◽  
Time Integration ◽  
Low Frequency ◽  
Second Order ◽  
Integration Scheme ◽  
Lumped Mass ◽  
Central Difference ◽  
Infinite Element ◽  
Time Integration Scheme ◽  
The Time Domain

We introduce an approach blending the Perfectly Matched Layer (PML) and infinite element paradigms, to achieve better performance and wider applicability than either approach alone. In this paper, we address the specific challenges of unbounded problems when using time-domain explicit finite elements: 1. The algorithm must be spatially local, to minimize storage and communication cost, 2. It must contain second-order time derivatives for compatibility with the explicit central-difference time integration scheme, 3. Its coefficient for the second-order derivatives must be diagonal (“lumped mass”), 4. It must be time-stable when used with central-differences, 5. It must converge to the correct low-frequency (Laplacian) limit, 6. It should exhibit high accuracy across typically encountered dynamic frequencies, i.e. at short to long wavelengths, 7. Its user interface should be as simple as possible. Here, we will describe the derivation of a time-domain implementation of the hybrid PML/infinite element, and discuss its advantages for implementation.

scholarly journals A Hybrid Time Integration Scheme for the Discontinuous Galerkin Discretizations of Convection-Dominated Problems

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 1870
Author(s):  
Liang Li ◽  
Songping Wu
Keyword(s):  
Discontinuous Galerkin ◽  
Time Integration ◽  
Integration Scheme ◽  
Hybrid Scheme ◽  
Time Step ◽  
Third Order ◽  
Element Size ◽  
Time Integration Scheme ◽  
Dg Method ◽  
Convection Dominated

Discontinuous Galerkin (DG) method is a popular high-order accurate method for solving unsteady convection-dominated problems. After spatially discretizing the problem with the DG method, a time integration scheme is necessary for evolving the result. Owing to the stability-based restriction, the time step for an explicit scheme is limited by the smallest element size within the mesh, making the calculation inefficient. In this paper, a hybrid scheme comprising a three-stage, third-order accurate, and strong stability preserving Runge–Kutta (SSP-RK3) scheme and the three-stage, third-order accurate, L-stable, and diagonally implicit Runge–Kutta (LDIRK3) scheme is proposed. By dealing with the coarse and the refined elements with the explicit and implicit schemes, respectively, the time step for the hybrid scheme is free from the limitation of the smallest element size, making the simulation much more efficient. Numerical tests and comparison studies were made to show the performance of the hybrid scheme.

scholarly journals Structural Reliability Sensitivities under Nonstationary Random Vibrations

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Rita Greco ◽  
Francesco Trentadue
Keyword(s):  
Structural Reliability ◽  
Structural Parameters ◽  
Time Integration ◽  
Structural Response ◽  
Integration Scheme ◽  
Structural Systems ◽  
Frame Building ◽  
Time Integration Scheme ◽  
Noise Input ◽  
The Time Domain

Response sensitivity evaluation is an important element in reliability evaluation and design optimization of structural systems. It has been widely studied under static and dynamic forcing conditions with deterministic input data. In this paper, structural response and reliability sensitivities are determined by means of the time domain covariance analysis in both classically and nonclassically damped linear structural systems. A time integration scheme is proposed for covariance sensitivity. A modulated, filtered, white noise input process is adopted to model the stochastic nonstationary loads. The method allows for the evaluation of sensitivity statistics of different quantities of dynamic response with respect to structural parameters. Finally, numerical examples are presented regarding a multistorey shear frame building.

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