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pro vyhledávání: '"Schnake, Stefan"'
In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the BGK equation for gas dynamics. The MM formulation represents a kinetic distri
Externí odkaz:
http://arxiv.org/abs/2410.00678
Autor:
Schnake, Stefan, Kendrick, Coleman, Endeve, Eirik, Stoyanov, Miroslav, Hahn, Steven, Hauck, Cory D, Green, David L, Snyder, Phil, Canik, John
Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov-Poisson-Lenard-Bernstein (VPLB) mod
Externí odkaz:
http://arxiv.org/abs/2402.06493
Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Gal
Externí odkaz:
http://arxiv.org/abs/2308.05914
Autor:
Hauck, Cory, Schnake, Stefan
In this paper, we present a predictor-corrector strategy for constructing rank-adaptive dynamical low-rank approximations (DLRAs) of matrix-valued ODE systems. The strategy is a compromise between (i) low-rank step-truncation approaches that alternat
Externí odkaz:
http://arxiv.org/abs/2209.00550
A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f = f(x,v,t)$ converges to an isotropic function $M(v)\rho(x,t)$, called the drift-diffusion limit, where $M$ is
Externí odkaz:
http://arxiv.org/abs/2206.09805
Autor:
Feng, Xiaobing, Schnake, Stefan
This paper establishes the optimal $H^1$-norm error estimate for a nonstandard finite element method for approximating $H^2$ strong solutions of second order linear elliptic PDEs in non-divergence form with continuous coefficients. To circumvent the
Externí odkaz:
http://arxiv.org/abs/1909.13803
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A "truncation" of Pascal's triangle is a triangular array of numbers that satisfies the usual Pascal recurrence but with a boundary condition that declares some terminal set of numbers along each row of the array to be zero. Presented here is a famil
Externí odkaz:
http://arxiv.org/abs/1807.08181
This paper is concerned with continuous and discrete approximations of $W^{2,p}$ strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form. The continuous approximation of these equations is achieve
Externí odkaz:
http://arxiv.org/abs/1801.05879
Autor:
Feng, Xiaobing, Schnake, Stefan
This paper develops an analogue (or counterpart) to discontinuous Galerkin (DG) methods for approximating a general class of calculus of variations problems. The proposed method, called the discontinuous Ritz (DR) method, constructs a numerical solut
Externí odkaz:
http://arxiv.org/abs/1709.04297