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[CT115]

CT115 (1/1) : Numerical methods for partial differential equations, boundary value problems (65N)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : Accurate numerical PDE solutions require good quality computational meshes on the corresponding geometric domains. Both explicitly and implicitly tangled meshes are problematic for finite element simulations as are meshes with low quality elements. In this talk, we will present our multiobjective optimization methods for mesh untangling and quality improvement of quadrilateral meshes. The objective functions are developed by combining separate objective functions using ``no articulation of preferences”. Encouraging results from numerical experiments will be presented.
Classification : 65N50, 65N30, 65K10
Format : Talk at Waseda University
Author(s) :
- Moein Moradi (University of Kansas)
- Suzanne Michelle Shontz (University of Kansas)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : The heterogeneous 2LM method, introduced in Loisel et al., SIAM J. Sci. Comput., 37, 2015, is a domain decomposition method where the coarse space is built using eigenvectors associated with subdomain eigenproblems. In this talk, we provide a new a-priori estimate for the norm of the coarse problem to guarantee further that the method is robust w.r.t the changes in the contrast of the diffusion coefficient. Numerical results are provided to support the theoretical findings.
Classification : 65N55, 65F10, 65N30, 65N22
Format : Talk at Waseda University
Author(s) :
- Hieu Nguyen (Fulbright University Vietnam)
- Sébastien Loisel (Heriot-Watt University)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : The Helmholtz equation is notoriously difficult to solve, especially for the case of high wavenumber. The Restricted Additive Schwarz preconditioner with local impedance problems, often called the ORAS method, is arguably the most successful one-level parallel method for Helmholtz problems. This preconditioner can be applied on very general geometries, does not require parameter-tuning, and can even be robust to increasing wavenumber. To date, there is relatively little convergence analysis for this method. In the talk, I will present a novel analysis of the ORAS method.
Classification : 65N55
Format : Talk at Waseda University
Author(s) :
- Shihua Gong (The Chinese University of Hong Kong, Shenzhen)

Session Time & Room : 5D (Aug.25, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : Elliptic boundary layer problems arise in many applications including fluid dynamics, gas dynamics, plate and shell problems in structural mechanics, modeling of semiconductor devices and many more. We propose a least-squares hp-spectral element method for 1D elliptic boundary layer problems. The regularity estimates are stated and the main stability theorem is obtained using non-conforming spectral element functions. For the hp-version we use a 3 element mesh which allows us to resolve the boundary layers completely by placing very thin needle like elements near the boundary layer and a coarse mesh away from the layer. Numerical scheme and error estimates are obtained which are robust i.e. independent of the boundary layer parameter and decay exponentially in terms of the degree of the approximating polynomials. Numerical results confirm convergence results with various combinations of the boundary layer thickness, degrees of the approximating polynomials, and layers in the mesh.
Classification : 65N35, 65N20, 65N50
Author(s) :
- Akhlaq Husain (Jamia Millia Islamia New Delhi)
- Akhlaq Husain (BML Munjal University Gurgaon)