Search results for "Mathematic"
showing 10 items of 24974 documents
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…
Measurement of dielectron production in central Pb-Pb collisions at √sNN = 2.76 TeV
2019
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. The first measurement of dielectron (e + e −) production in central (0 – 10 %) Pb – Pb collisions at √sNN=2.76TeV at the LHC is presented. The dielectron invariant-mass spectrum is compared to the expected contributions from hadron decays in the invariant-mass range 0 < mee < 3.5 GeV / c2. The ratio of data and the cocktail of hadronic contributions without vacuum ρ0 is measured in the invariant-mass range 0.15 < mee < 0.7 GeV / c2, w…
Applying Axial Symmetries to Historical Silk Fabrics: SILKNOW’s Virtual Loom
2020
Symmetry is part of textile art in patterns and motifs that decorate fabrics, which are made by the interlacement of warp and wefts. Moreover, the 3D representation of fabrics have already been studied by some authors
A Perturbed Cauchy Viscoelastic Problem in an Exterior Domain
2023
A Cauchy viscoelastic problem perturbed by an inverse-square potential, and posed in an exterior domain of RN, is considered under a Dirichlet boundary condition. Using nonlinear capacity estimates specifically adapted to the non-local nature of the problem, the potential function and the boundary condition, we establish sufficient conditions for the nonexistence of weak solutions.
Game-Theoretic Approach to Hölder Regularity for PDEs Involving Eigenvalues of the Hessian
2021
AbstractWe prove a local Hölder estimate for any exponent $0<\delta <\frac {1}{2}$ 0 < δ < 1 2 for solutions of the dynamic programming principle $$ \begin{array}{@{}rcl@{}} u^{\varepsilon} (x) = \sum\limits_{j=1}^{n} \alpha_{j} \underset{\dim(S)=j}{\inf} \underset{|v|=1}{\underset{v\in S}{\sup}} \frac{u^{\varepsilon} (x + \varepsilon v) + u^{\varepsilon} (x - \varepsilon v)}{2} \end{array} $$ u ε ( x ) = ∑ j = 1 n α j inf dim ( S ) = j sup v ∈ S | v | = 1 u ε ( x + ε v ) + u ε ( x − ε v ) 2 with α1,αn > 0 and α2,⋯ ,αn− 1 ≥ 0. The proof is based on a new coupling idea from game theory. As an application, we get the same regularity estimate for viscosity solutions of the PDE $…
Equivalence of viscosity and weak solutions for a $p$-parabolic equation
2019
AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p>1$$ p > 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .
Hölder gradient regularity for the inhomogeneous normalized p(x)-Laplace equation
2022
We prove the local gradient Hölder regularity of viscosity solutions to the inhomogeneous normalized p(x)-Laplace equation −Δp(x)Nu=f(x), where p is Lipschitz continuous, infp>1, and f is continuous and bounded. peerReviewed
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.