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[CT092]

CT092 (1/1) : Numerical approximation and computational geometry (primarily algorithms) (65D) / Stochastic analysis (60H)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : Layer potentials, integrals representing the solution of a PDE when solved using boundary integral methods, are notoriously difficult to accurately evaluate close to the boundary of the domain due to a rapidly varying integrand. The presented quadrature method resolves this key challenge by factoring the integrand into a smooth and a simpler nearly singular part, then efficiently expanding the smooth part in a new basis and treating the remaining nearly singular integrals analytically.
Classification : 65D32, 65D30, 65R20, 65N99
Format : Talk at Waseda University
Author(s) :
- David Krantz (KTH Royal Institute of Technology)
- Anna-Karin Tornberg (KTH Royal Institute of Technology)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : Approximate formula for indefinite convolutions by means of the Sinc approximation has been proposed by Stenger. The formula is based on his Sinc indefinite integration formula combined with the single-exponential transformation. Recently, the Sinc indefinite integration formula was improved by replacing the single-exponential transformation with the double-exponential transformation. Based on the improved formula, this study proposes a new approximate formula for indefinite convolutions.
Classification : 65D05, 65D15, 65D30, 65D32
Format : Online Talk on Zoom
Author(s) :
- Tomoaki Okayama (Hiroshima City University)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : Finite volume, weighted essentially non-oscillatory (WENO) schemes using the simple smoothness indicator $\sigma= 1/(L-1) \sum_{j} (u_{j} - u_{m})^2$, are presented, where $L$ is the number of mesh elements in the stencil, $u_j$ is the local function average over $j$th element, and index $m$ gives the target element. We develop a modification of WENO-Z weighting that gives a reliable and accurate reconstruction of adaptive order. Convergence results are proved. Numerical experimental results are also provided.
Classification : 65D15, 65M08, 65M12, 76M12
Format : Online Talk on Zoom
Author(s) :
- Chiehsen Huang (National Sun Yat-sen University)
- Todd Arbogast (University of Texas; Austin)
- Chenyu Tian (University of Texas; Austin)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : We introduce an algorithm for Tchakaloff-like compression of Quasi-Monte Carlo (QMC) volume or surface integration of bivariate and trivariate compact domains. The key tools of the algorithm are Davis-Wilhelmsen theorem on the so-called “Tchakaloff sets” for positive linear functionals on polynomial spaces, and Lawson-Hanson algorithm for NNLS. We provide various examples, focusing, in particular, on the compression of volume and surface integration on union of balls.
Classification : 65D32, 65D30
Format : Online Talk on Zoom
Author(s) :
- Giacomo Elefante (University of Padova)
- Alvise Sommariva (University of Padova)
- Marco Vianello (University of Padova)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E704
Type : Contributed Talk
Abstract : In this paper, we study the convergence of numerical solution of Reflected Backward Stochastic Equations (RBSDEs) by the penalisation approach and we apply this on the pricing problem of American option. Usually the obstacle-related problem is studied by Snell Envelope and penalisation is used on proving existence. Here we fill the gap between penalisation and numerical solution. As result, we proved successfully the convergence rate for both continuous and discrete penalised solution.
Classification : 60Hxx, 65Cxx, 60H35, 65C30, 60G40
Format : Talk at Waseda University
Author(s) :
- Wanqing WANG (Ecole Polytechnique)
- Emmanuel Gobet (Ecole Polytechnique)
- Mingyu Xu (Fudan University)