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[CT093]

CT093 (1/1) : Numerical approximation and computational geometry (primarily algorithms) (65D) / Mechanics of particles and systems (70-) / Markov processes (60J)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
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
Format : Talk at Waseda University
Author(s) :
- Lei Wang (University of Wisconsin, Milwaukee)
- Robert Krasny (University of Michigan, Ann Arbor)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
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
Format : Talk at Waseda University
Author(s) :
- Daisuke Furihata (Osaka University)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
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
Format : Talk at Waseda University
Author(s) :
- Saad Benjelloun (Makhbar Mathematical Sciences Research institute)
- saad benjelloun (Makhbar institute)
- Abdellah Chkifa (UM6P)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
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
Format : Talk at Waseda University
Author(s) :
- Jiefei Yang (The University of Hong Kong)
- Guanglian Li (The University of Hong Kong)

Session Time & Room : 4C (Aug.24, 13:20-15:00) @E507
Type : Contributed Talk
Abstract : This study provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. We showed the spatial distribution of the model compartments when the basic reproduction rate R0 < 1 and R0 > 1. We demonstrate the model's effectiveness by performing numerical simulations and then investigated the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19 epidemic.
Classification : 60J70, 62H12, 00A71
Format : Talk at Waseda University
Author(s) :
- Kayode Oshinubi (Northern Arizona University)
- Jacques Demongeot (University of Grenoble Alpes)
- Brice Kammegne (University of Dschang )