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Professor MIKHAIL TRETYAKOV's Outputs (26)

Stochastic resin transfer molding process (2017)
Journal Article
Park, M., & Tretyakov, M. (in press). Stochastic resin transfer molding process. SIAM/ASA Journal on Uncertainty Quantification, 5(1), https://doi.org/10.1137/16M1096578

We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in t... Read More about Stochastic resin transfer molding process.

Layer methods for stochastic Navier–Stokes equations using simplest characteristics (2016)
Journal Article
Milstein, G., & Tretyakov, M. (2016). Layer methods for stochastic Navier–Stokes equations using simplest characteristics. Journal of Computational and Applied Mathematics, 302, https://doi.org/10.1016/j.cam.2016.01.051

We propose and study a layer method for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploit... Read More about Layer methods for stochastic Navier–Stokes equations using simplest characteristics.

Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise (2015)
Journal Article
Zhang, Z., Tretyakov, M., Rozovskii, B., & Karniadakis, G. E. (2015). Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise. SIAM Journal on Numerical Analysis, 53(1), Article 153-183. https://doi.org/10.1137/130932156

We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multistage algorithm for long-time integration. We derive... Read More about Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise.

A recursive sparse grid collocation method for differential equations with white noise (2014)
Journal Article
Zhang, Z., Tretyakov, M., Rozovskii, B., & Karniadakis, G. E. (2014). A recursive sparse grid collocation method for differential equations with white noise. SIAM Journal on Scientific Computing, 36(4), A1652–A1677. https://doi.org/10.1137/130938906

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first an... Read More about A recursive sparse grid collocation method for differential equations with white noise.

On the long-time integration of stochastic gradient systems (2014)
Journal Article
Leimkuhler, B., Matthews, C., & Tretyakov, M. (2014). On the long-time integration of stochastic gradient systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470(2170), Article 20140120. https://doi.org/10.1098/rspa.2014.0120

This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic (stepsize... Read More about On the long-time integration of stochastic gradient systems.