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[CT093]

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : We present theoretical and practical aspects on the development of accurate surrogate models from first-principles, multiscale, PDE models for industrial chemico-physical processes. We will present many applications in Phosphate industry done in collaboration with OCP-Group in Morocco. The surrogate models are based on sparse multivariate polynomial interpolation. The goal is to reduce the computational time while preserving its physical properties such as monotonicity and positivity.
Classification : 65D40, 65D05
Author(s) :
- Saad Benjelloun (Makhbar Mathematical Sciences Research institute)
- saad benjelloun (Makhbar institute)
- Abdellah Chkifa (UM6P)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : We introduce a sparse grid interpolation and quadrature scheme for pricing multi-asset American option based on dynamic programming. At each time step, we take advantage of the smoothness of the continuation value function, allowing for fast convergence of interpolation. In the multi-dimensional spatial domain, conditional expectations are estimated by sparse grid quadrature or QMC, depending on the asset models. Our algorithm is proven to have accurate error estimates, and numerical experiments demonstrate its efficiency.
Classification : 65D40, 65Kxx
Author(s) :
- Jiefei Yang (The University of Hong Kong)
- Guanglian Li (The University of Hong Kong)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : Brownian Dynamics simulations require correlated random displacements ${\bf g} = \sqrt{D}{\bf z}$ to account for hydrodynamic interactions among solvated biomolecules and polymers, where $D$ is the diffusion matrix based on the Rotne-Prager-Yamakawa tensor and ${\bf z}$ is a normal random vector. The Spectral Lanczos Decomposition Method (SLDM) computes a sequence of approximations to ${\bf g}$, but each iteration requires a matrix-vector product $D{\bf q}_k$, where ${\bf q}_k$ is the $k$th Lanczos vector. The present work applies the barycentric Lagrange treecode (BLTC) to accelerate the matrix-vector product, and numerical results show the performance of the SLDM-BLTC in serial and parallel calculations.
Classification : 65D99, 65Z05, 65F60, 76M35
Author(s) :
- Lei Wang (University of Wisconsin, Milwaukee)
- Robert Krasny (University of Michigan, Ann Arbor)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : In this talk we will present an efficient meshless numerical approach for solving space-time fractional partial differential equations (STFPDEs). The method of (inverse) Laplace transform is applied on time Caputo fractional derivative. The localized radial basis function collocation method (LRBFCM) is then used to derive a discretization scheme for the space Riemann-Liouville fractional derivatives on scattered nodes. Several numerical examples are presented to illustrate the validity and feasibility of the proposed numerical method.
Classification : 65Dxx, 65R20, 26A33
Author(s) :
- Dongfang Yun (Central South University)

Session Date & Time : 4C (Aug.24, 13:20-15:00)
Type : Contributed Talk
Abstract : The Cahn-Hilliard equation describes phase separation phenomena well. It has been proven that this solution converges to one of the Hele-Shaw problems in the limit of one coefficient parameter to zero, which is mathematically satisfactory as an order-reduction result. However, the computation of the Hele-Shaw problem is also problematic. Therefore, we observed the coarsening process of phase separation phenomena and subsequently considered a particle dynamics model that roughly reproduces the process.
Classification : 70-10, 65N06, 65N08
Author(s) :
- Daisuke Furihata (Osaka University)