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[CT110]

CT110 (1/1) : Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M) / Applications to the sciences (65Z) / Partial differential equations of mathematical physics and other areas of application (35Q)

Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : We derive a PDE model for American derivatives' pricing including the valuation adjustment (XVA), assuming mean-reverting default risk for the counterparty, and constant default risk for the self-party. There are two nonlinear source terms, one from the American constraint and one from the XVA, handled by a double-penalty iteration. We also derive asymptotic approximations to the XVA price and to the free boundary. We present numerical experiments to study the accuracy and effectiveness of the 2D PDE and asymptotic approximations.
Classification : 65Mxx, 65Nxx, 91Gxx
Format : Talk at Waseda University
Author(s) :
- Christina Christara (University of Toronto)
- Yuwei Chen (University of Toronto)

Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : X-rays Computed Tomography is a main pillar of medical imaging which at present is experiencing a strong innovation phase. While new tomographic systems try to minimize X-rays exposure, non-trivial challenges exist, mainly increased noise levels and the need for dealing with low and high contrast regions. In this talk we will refer about our research on new algorithms able to efficiently deal with this trade–off, with specific reference to Diffuse Optical Tomography.
Classification : 65Z05, 65N20, 65N80, 68T07
Format : Talk at Waseda University
Author(s) :
- Paola Causin (University of Milano )
- Andrea Aspri (University of Milano )

Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : Solving the time-independent Schrödinger equation gives us full access to the chemical properties of molecules. Among all the ab-initio methods, full configuration interaction (FCI) provides the numerically exact solution under a predefined basis set. However, the FCI problem scales factorially with respect to the number of bases and electrons and suffers from the curse of dimensionality. The FCI problem could be reformulated as an unconstraint minimization problem. This work proposes a novel algorithm to address the minimization problem. The algorithm introduces an extra search dimension to enable the exact linesearch for the multi-coordinate descent method, which could be fully parallelized. Hence, the proposed algorithm benefits from both exact linesearch and parallelization. Numerically, we demonstrate the parallel efficiency of the algorithm. The algorithm achieves better energy and parallelism on systems with approximately a hundred electrons than other existing methods.
Classification : 65Z05, 68Q12
Format : Talk at Waseda University
Author(s) :
- Yuejia Zhang (Fudan University)
- Yingzhou Li (Fudan University)

Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : Bilayered cathodes are promising candidates to improve lithium-ion battery performance by optimising the electrode design. In this work, lithium iron phosphate and nickel manganese cobalt chemistries are connected in two discrete layers within a cathode, which improves the C-rate performance above 2C compared to uniform cells. To inform the design process we create mathematical model to accommodate multilayers. The model is solved numerically, validated against data and explains how each layer acts.
Classification : 35Qxx, 37Nxx
Format : Talk at Waseda University
Author(s) :
- Eloise Tredenick (University of Oxford)

Session Time & Room : 2D (Aug.22, 15:30-17:10) @E709
Type : Contributed Talk
Abstract : Melanoma routinely develops resistance to targeted therapies, leading to unfavourable prognosis for patients. We introduce a novel approach to modelling single-cell RNA-seq data obtained from melanoma tumours, using partial differential equations (PDEs) to represent the tumour as a spatio-structural population. We show how non-spatial data can be used to predict spatially heterogeneous distributions of cell types, within the tumour, and explore combination therapies and treatment strategies to overcome traditional patterns of resistance.
Classification : 35Q92, 37N25, 62P10, 92-10, 35G20, Mathematical Oncology, PDEs
Author(s) :
- Arran Hodgkinson (Queen's University Belfast)
- Arran Hodgkinson (Queen's University Belfast)
- Dumitru Trucu (University of Dundee)
- Matthieu Lacroix (Institut de Recherche en Cancerologie de Montpellier)
- Laurent Le Cam (Institut de Recherche en Cancerologie de Montpellier)
- Ovidiu Radulescu (Universite de Montpellier)