EXAHD: An Exa-Scalable Two-Level Sparse Grid Approach for Higher-Dimensional Problems in Plasma Physics and Beyond

2018 ◽  
pp. 513-529 ◽  
Author(s):  
Mario Heene ◽  
Alfredo Parra Hinojosa ◽  
Michael Obersteiner ◽  
Hans-Joachim Bungartz ◽  
Dirk Pflüger
Keyword(s):  
Plasma Physics ◽  
Sparse Grid ◽  
Grid Approach ◽  
Higher Dimensional

EXAHD: An Exa-scalable Two-Level Sparse Grid Approach for Higher-Dimensional Problems in Plasma Physics and Beyond

2014 ◽  
pp. 565-576 ◽  
Author(s):  
Dirk Pflüger ◽  
Hans-Joachim Bungartz ◽  
Michael Griebel ◽  
Frank Jenko ◽  
Tilman Dannert ◽  
...  
Keyword(s):  
Plasma Physics ◽  
Sparse Grid ◽  
Grid Approach ◽  
Higher Dimensional

Sparse Grid Approach to Accelerate Particle-In-Cell Technique: Application to the Hall Thruster E×B Instability *

2021 ◽  
Author(s):  
L. Garrigues ◽  
M. Chung-To-Sang ◽  
G. Fubiani ◽  
C. Guillet ◽  
F. Deluzet ◽  
...  
Keyword(s):  
Sparse Grid ◽  
Hall Thruster ◽  
Accelerate Particle ◽  
Particle In Cell ◽  
Grid Approach

scholarly journals A sparse grid approach to balance sheet risk measurement

2019 ◽  
Vol 65 ◽  
pp. 236-265
Author(s):  
Cyril Bénézet ◽  
Jérémie Bonnefoy ◽  
Jean-François Chassagneux ◽  
Shuoqing Deng ◽  
Camilo Garcia Trillos ◽  
...  
Keyword(s):  
Numerical Method ◽  
Balance Sheet ◽  
Gaussian Model ◽  
Sparse Grid ◽  
Risk Indicators ◽  
Insurance Company ◽  
Numerical Estimation ◽  
Grid Approximation ◽  
Grid Approach ◽  
Stochastic Interest

In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & choles model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.

scholarly journals Faber-Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Shu-Li Mei
Keyword(s):  
Option Pricing ◽  
Nonlinear Partial Differential Equations ◽  
Variational Iteration Method ◽  
Sparse Approximation ◽  
Second Order ◽  
Sparse Grid ◽  
Transformation Model ◽  
Approximation Solution ◽  
Grid Approach ◽  
Definition Of

Transforming the nonlinear Black-Scholes equation into the diffusion PDE by introducing the log transform ofSand(T−t)→τcan provide the most stable platform within which option prices can be evaluated. The space jump that appeared in the transformation model is suitable to be solved by the sparse grid approach. An adaptive sparse approximation solution of the nonlinear second-order PDEs was constructed using Faber-Schauder wavelet function and the corresponding multiscale analysis theory. First, we construct the multiscale wavelet interpolation operator based on the definition of interpolation wavelet theory. The operator can be used to discretize the weak solution function of the nonlinear second-order PDEs. Second, using the couple technique of the variational iteration method (VIM) and the precision integration method, the sparse approximation solution of the nonlinear partial differential equations can be obtained. The method is tested on three classical nonlinear option pricing models such as Leland model, Barles-Soner model, and risk adjusted pricing methodology. The solutions are compared with the finite difference method. The present results indicate that the method is competitive.

scholarly journals Option pricing with a direct adaptive sparse grid approach

2012 ◽  
Vol 236 (15) ◽  
pp. 3741-3750 ◽  
Author(s):  
Hans-Joachim Bungartz ◽  
Alexander Heinecke ◽  
Dirk Pflüger ◽  
Stefanie Schraufstetter
Keyword(s):  
Option Pricing ◽  
Sparse Grid ◽  
Grid Approach

Addressing global uncertainty and sensitivity in first-principles based microkinetic models by an adaptive sparse grid approach

2018 ◽  
Vol 148 (3) ◽  
pp. 034102 ◽  
Author(s):  
Sandra Döpking ◽  
Craig P. Plaisance ◽  
Daniel Strobusch ◽  
Karsten Reuter ◽  
Christoph Scheurer ◽  
...  
Keyword(s):  
First Principles ◽  
Sparse Grid ◽  
Grid Approach ◽  
Global Uncertainty

scholarly journals Solution of Time-dependent Advection-Diffusion Problems with the Sparse-grid Combination Technique and a Rosenbrock Solver

2001 ◽  
Vol 1 (1) ◽  
pp. 86-98 ◽  
Author(s):  
Boris Lastdrager ◽  
Barry Koren ◽  
Jan Verwer
Keyword(s):  
Time Integration ◽  
Size Control ◽  
Sparse Grid ◽  
Time Dependent ◽  
Step Size ◽  
Combination Technique ◽  
Burgers Equations ◽  
Advection Diffusion ◽  
Grid Approach ◽  
Diffusion Problems

Abstract In the current paper the efficiency of the sparse-grid combination tech- nique applied to time-dependent advection-diffusion problems is investigated. For the time-integration we employ a third-order Rosenbrock scheme implemented with adap- tive step-size control and approximate matrix factorization. Two model problems are considered, a scalar 2D linear, constant-coe±cient problem and a system of 2D non- linear Burgers' equations. In short, the combination technique proved more efficient than a single grid approach for the simpler linear problem. For the Burgers' equations this gain in efficiency was only observed if one of the two solution components was set to zero, which makes the problem more grid-aligned.

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