Search results for "010101 applied mathematics"
showing 6 items of 676 documents
Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models
2016
American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed
Designing a graphics processing unit accelerated petaflop capable lattice Boltzmann solver: Read aligned data layouts and asynchronous communication
2016
The lattice Boltzmann method is a well-established numerical approach for complex fluid flow simulations. Recently, general-purpose graphics processing units (GPUs) have become available as high-performance computing resources at large scale. We report on designing and implementing a lattice Boltzmann solver for multi-GPU systems that achieves 1.79 PFLOPS performance on 16,384 GPUs. To achieve this performance, we introduce a GPU compatible version of the so-called bundle data layout and eliminate the halo sites in order to improve data access alignment. Furthermore, we make use of the possibility to overlap data transfer between the host central processing unit and the device GPU with com…
Hölder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian
2018
In this paper, we study an evolution equation involving the normalized [Formula: see text]-Laplacian and a bounded continuous source term. The normalized [Formula: see text]-Laplacian is in non-divergence form and arises for example from stochastic tug-of-war games with noise. We prove local [Formula: see text] regularity for the spatial gradient of the viscosity solutions. The proof is based on an improvement of flatness and proceeds by iteration.
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
Fractional Hardy inequalities and visibility of the boundary
2013
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.