Papers by Danail Vassilev
Computer Methods in Applied Mechanics and Engineering, 2017
A multiscale flux basis algorithm is developed for the Stokes-Darcy flow problem. The method is b... more A multiscale flux basis algorithm is developed for the Stokes-Darcy flow problem. The method is based on a non-overlapping domain decomposition algorithm, where the global problem is reduced to a coarse scale mortar interface problem that is solved by an iterative solver. Subdomain solves are required at each interface iteration, so the cost for the method without a multiscale basis can be high when the number of subdomains or the condition number of the interface problem is large. The proposed algorithm involves precomputing a multiscale flux basis, which consists of the flux (or velocity trace) response from each mortar degree of freedom. It is computed by each subdomain independently before the interface iteration begins. The subdomain solves required at each iteration are substituted by a linear combination of the multiscale basis. This may lead to a significant reduction in computational cost since the number of subdomain solves is fixed, depending only on the number of mortar degrees of freedom associated with a subdomain. Several numerical examples are carried out to demonstrate the efficiency of the multiscale flux basis implementation for large-scale Stokes-Darcy problems.
whose course on partial differential equations intensified my interest in the field and greatly i... more whose course on partial differential equations intensified my interest in the field and greatly influenced my decision to pursue a Ph.D. in Mathematics. Many thanks to all the friends and colleagues at the Department of Mathematics at Pitt, especially to Evandro and Carolina Manica, Gergina Pencheva, Evgueni Trofimov, and Ben Ganis for creating a warm and inspiring atmosphere. I would also like to thank my parents and my brother Stanislav for their constant love and support. Above all, I thank my wife Ralitsa whose love, patience and understanding give me strength to be successful. x
Monthly Weather Review, 2015
An important question for atmospheric modeling is the viability of semi-implicit time integration... more An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge–Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank–Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On t...
SIAM Journal on Scientific Computing, 2009
A mathematical and numerical model describing chemical transport in a Stokes-Darcy flow system is... more A mathematical and numerical model describing chemical transport in a Stokes-Darcy flow system is discussed. The flow equations are solved through domain decomposition using classical finite element methods in the Stokes region and mixed finite element methods in the Darcy region. The local discontinuous Galerkin (LDG) method is used to solve the transport equation. Models dealing with coupling between Stokes and Darcy equations have been extensively discussed in the literature. This paper focuses on the approximation of the transport equation. Stability of the LDG scheme is analyzed, and an a priori error estimate is proved. Several numerical examples verifying the theory and illustrating the capabilities of the method are presented.
Numerische Mathematik, 2013
We investigate mortar multiscale numerical methods for coupled Stokes and Darcy flows with the Be... more We investigate mortar multiscale numerical methods for coupled Stokes and Darcy flows with the Beavers-Joseph-Saffman interface condition. The domain is decomposed into a series of subdomains (coarse grid) of either Stokes or Darcy type. The subdomains are discretized by appropriate Stokes or Darcy finite elements. The solution is resolved locally (in each coarse element) on a fine scale, allowing for non-matching grids across subdomain interfaces. Coarse scale mortar finite elements are introduced on the interfaces to approximate the normal stress and impose weakly continuity of the normal velocity. Stability and a priori error estimates in terms of the fine subdomain scale h and the coarse mortar scale H are established for fairly general grid configurations, assuming that the mortar space satisfies a certain inf-sup condition. Several examples of such spaces in two and three dimensions are given. Numerical experiments are presented in confirmation of the theory.
Numerische Mathematik, 2013
We study locally mass conservative approximations of coupled Darcy and Stokes flows on polygonal ... more We study locally mass conservative approximations of coupled Darcy and Stokes flows on polygonal and polyhedral meshes. The discontinuous Galerkin (DG) finite element method is used in the Stokes region and the mimetic finite difference method is used in the Darcy region. DG finite element spaces are defined on polygonal and polyhedral grids by introducing lifting operators mapping mimetic degrees of freedom to functional spaces. Optimal convergence estimates for the numerical scheme are derived. Results from computational experiments supporting the theory are presented.
Computer Methods in Applied Mechanics and Engineering, 2014
A non-overlapping domain decomposition method is presented to solve a coupled Stokes-Darcy flow p... more A non-overlapping domain decomposition method is presented to solve a coupled Stokes-Darcy flow problem in parallel by partitioning the computational domain into multiple subdomains, upon which families of coupled local problems of lower complexity are formulated. The coupling is based on appropriate interface matching conditions. The global problem is reduced to an interface problem by eliminating the interior subdomain variables. The interface problem is solved by an iterative procedure, which requires solving subdomain problems at each iteration. Finite element techniques appropriate for the type of each subdomain problem are used to discretize it. The condition number of the resulting algebraic system is analyzed and numerical tests verifying the theoretical estimates are provided.
COUPLED VI : proceedings of the VI International Conference on Computational Methods for Coupled Problems in Science and Engineering, 2015
Motor manufacturers are facing a difficult challenge in designing traction motors for the latest ... more Motor manufacturers are facing a difficult challenge in designing traction motors for the latest generation of hybrid and all-electric vehicles. The efficiency with which these motors can perform is critical, as it impacts on the vehicle range and battery life. Many of the issues involved in the motor design have a complex nature which requires multiple fields of physics such as electromagnetics (EM), mechanics and thermal analysis. All these physics are usually interdependent and have to be considered collectively in order to obtain optimal performance for a particular scenario. This paper presents a multiphysics simulation tool that was implemented to address this situation. The Opera FEA software suite [1] was developed to include a multiphysics analysis that can link several EM, thermal and stress analyses. Opera's Machines Environment (parameterised template software for designing motors and generators) has been extended to allow easy setup of coupled multiphysics analyses such as EM to thermal and EM to stress. In order to further facilitate the coupling of different analyses, a link to the Python programming language was embedded in Opera FEA software. The embedded Python facility offers options to perform certain post-processing operations during the solving stage and hence allow data transfer between different stages of the multiphysics analysis. It also extends Opera's capabilities to interact with other FEA software. 1 INTRODUCTION With growing concerns over future petroleum supplies and air pollution, sustainable transportation has emerged as a vital mission for countries that seek to expand infrastructure 428 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by UPCommons. Portal del coneixement obert de la UPC
Please cite this article as: B. Ganis, D. Vassilev, C. Wang, I. Yotov, A multiscale flux basis fo... more Please cite this article as: B. Ganis, D. Vassilev, C. Wang, I. Yotov, A multiscale flux basis for mortar mixed discretizations of Stokes-Darcy flows, Comput. Methods Appl. Mech. Engrg. (2016), http://dx.
An important question for atmospheric modeling is the viability of semi-implicit time integration... more An important question for atmospheric modeling is the viability of semi-implicit time integration schemes on massively parallel computing architectures. Semi-implicit schemes can provide increased stability and accuracy. However, they require the solution of an elliptic problem at each time step, creating concerns about their parallel efficiency and scalability. Here, a semi-implicit (SI) version of the Model for Prediction Across Scales (MPAS) is developed and compared with the original model version, which uses a split Runge-Kutta (SRK3) time integration scheme. The SI scheme is based on a quasi-Newton iteration toward a Crank-Nicolson scheme. Each Newton iteration requires the solution of a Helmholtz problem; here, the Helmholtz problem is derived, and its solution using a geometric multigrid method is described. On two standard test cases, a midlatitude baroclinic wave and a small-planet nonhydrostatic gravity wave, the SI and SRK3 versions produce almost identical results. On the baroclinic wave test, the SI version can use somewhat larger time steps (about 60%) than the SRK3 version before losing stability. The SI version costs 10%-20% more per step than the SRK3 version, and the weak and strong scalability characteristics of the two versions are very similar for the processor configurations the authors have been able to test (up to 1920 processors). Because of the spatial discretization of the pressure gradient in the lowest model layer, the SI version becomes unstable in the presence of realistic orography. Some further work will be needed to demonstrate the viability of the SI scheme in this case.
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Papers by Danail Vassilev