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[CT094]

Session Date & Time : 2D (Aug.22, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk, we will present a pseudospectral method for 2D advection operators. After discretizing the 2D advection operator by the Legendre-Gauss-Lobatto pseudospectral methods, we obtain a Sylvester equation. The Sylvester equation is equivalent to a block tridiagonal liner system of equations. We propose a URV approach to solve the linear system.
Classification : 65F05, 65N35
Author(s) :
- Yung-Ta Li (Fu Jen Catholic University)

Session Date & Time : 2D (Aug.22, 15:30-17:10)
Type : Contributed Talk
Abstract : When designing preconditioners based on domain decomposition methods, the coarse space plays a key role. In order to keep the scalability, the coarse space of low computational complexity is essential. We introduce a new coarse space of reduced dimension for vector field problems. Numerical results for the problems in three dimensions are also presented.
Classification : 65F08, 65F10, 65N30, 65N55
Author(s) :
- Duk-Soon Oh (Chungnam National University)

Session Date & Time : 2D (Aug.22, 15:30-17:10)
Type : Contributed Talk
Abstract : This work presents a new algebraic formulation for the Multiscale Robin Coupled Method - MRCM. This domain decomposition method generalizes other mixed multiscale methods by imposing Robin-type boundary conditions on the local problems. The MRCM is flexible and accurate, obtaining near-optimal scalability up to billions of unknowns in high-performance simulations. We propose a new algebraic formulation, allowing the construction of multiscale-based preconditioners for solving non-symmetric linear systems with Krylov subspace methods, such as GMRES.
Classification : 65F08, 65N55, 65N08, 76S05
Author(s) :
- Fabricio Simeoni de Sousa (University of Sao Paulo)
- Franciane F. Rocha (Wikki Brazil)
- Luca Meacci (Università degli Studi di Firenze)
- Rafael T. Guiraldello (Piri Technologies LLC)
- Roberto F. Ausas (University of Sao Paulo)
- Gustavo C. Buscaglia (University of Sao Paulo)
- Felipe Pereira (The University of Texas at Dallas)

Session Date & Time : 2D (Aug.22, 15:30-17:10)
Type : Contributed Talk
Abstract : Gauging the distance between a mixed state and its nearest separable state is important but challenging in the quantum mechanical system. We, in this talk, propose a dynamical system approach to tackle low-rank approximation of entangled bipartite systems, which has several advantages, including 1) A gradient dynamics in the complex space can be described in a fairly concise way; 2) The global convergence from any starting point to a local solution is guaranteed; 3) The requirement that the combination coefficients of pure states must be a probability distribution can be ensured; 4) The rank can be dynamically adjusted. The theory, algorithms, and some numerical experiments will be presented in this talk.
Classification : 65F10, 15A24, 65H10, 15A72, 58D19
Author(s) :
- Matthew M. Lin (National Cheng Kung University)
- Moody T. Chu (North Carolina State University)

Session Date & Time : 2D (Aug.22, 15:30-17:10)
Type : Contributed Talk
Abstract : We present a fully parallelizable preconditioner for the all-at-once linear system arising when an implicit Runge-Kutta method is employed for the time discretization of evolutionary PDEs. The triangular preconditioner for the resulting $2 \times 2$ block linear system entails a block-diagonal solve for all the stages and for all the time-steps, and a Schur complement in which a new block-preconditioner for the stage solver, based on the SVD of the RK coefficient matrix, is introduced.
Classification : 65F10, 65M22, 65Y05
Author(s) :
- Luca Bergamaschi (University of Padua)