The Southern Ontario Numerical Analysis Day (SONAD) is an annual one-day conference that brings together researchers (faculty, graduate students, postdoctoral fellows, and visitors) working in broad areas of numerical analysis and scientific computing at Ontario universities. The Department of Electrical and Computer Engineering at McMaster University is pleased to host SONAD in its 40th year.
We invite researchers to submit abstracts for 10-20-minute presentations. Presentations details will be announced to authors. For submission, see registration form. If the need arises, e-mail cheshmi@mcmaster.ca.
Deadline for submission of abstracts: May 17, 2025 May 22, 2025
Acceptance emails will be sent May 20-22 May 23-25
Evaluation Criteria: We try to have a good distribution of talks across schools, departments, research groups, topics and also give some priority to grad students, especially Ph.D. students. If we receive too many submissions to fit in the day, we may have to reduce the duration of the presentation, and/or select a limited number of submissions from topics, schools, departments, research groups with many submissions.
Registration is free but mandatory, and must be done through the registration form.
Deadline for registration: May 26, 2025.
Principal Research Scientist, Autodesk Research, Toronto
Title: Constrained Shape Gradients in Level-Set Topology Optimization: Bridging Geometry and Design
Abstract: This talk explores the integration of shape calculus and constrained optimization within the level-set framework for topology optimization. We explore the mathematical derivation of shape gradients in non-parametric, boundary-based approaches, highlighting the differential geometric complexities involved. Building upon this foundation, we introduce a novel framework that enables highly constrained shape updates along specified boundary components, accommodating affine transformations such as translation, rotation, and scaling. This approach is particularly beneficial for engineering applications requiring the preservation of specific geometric features, like maintaining a circular aperture for a pin connection while optimizing the surrounding structure. Central to our method is the Constrained Hilbert Space Extension, which ensures that the generated velocity fields for shape evolution adhere to imposed constraints while promoting descent directions for the objective function. Through canonical examples, we demonstrate the efficacy of this framework in achieving design objectives that balance flexibility and constraint, offering new avenues for advanced engineering design.
Associate Professor, University of Toronto
Title: High-Accuracy Computation for Electrical Impedance Tomography
Abstract: Electrical impedance tomography is a medical imaging technique that uses electric currents and potential measurements on the surface of the body to infer the electrical conductivity within the body. This is the classical mathematical problem of Calderón. We make the biologically reasonable assumption that the conductivity is piecewise constant. Our numerical approach to the inverse problem involves many solves of the forward problem which necessitates a fast and accurate numerical method for an elliptic interface problem for the electrostatic potential. We also impose the complete electrode model boundary condition which assumes no current off of electrodes and that the current through an electrode experiences a contact impedance before entering the body. We employ a boundary integral equation method and represent the potential as a sum of single layer potentials. The fast multiple method is used to accelerate the generalized minimal residual method for solving the integral equations. The integral equations are weakly singular as a result of the Green's function. The mixed boundary condition from the complete electrode model introduces another singularity at the edge of the electrodes. Our analysis reveals the nature of this singularity, which we exploit using generalized Gaussian quadrature. For the three dimensional problem, we use triangulated surfaces and the boundary element method. We obtain new analytical formulas for the integrals over triangles and develop a new geometric method for numerically computing integrals over triangles that uses geometric information of the true surface of integration. We expect our fast and accurate solver for the forward problem to lead to better reconstructions in electrical impedance tomography.
Professor, McMaster University
Title: Multiple Access Computation Offloading
Abstract: The provision of computing infrastructure at the “edges” of a wireless network would enable light weight devices to expand their capabilities by offloading latency-sensitive tasks. Potential applications include augmented reality systems, autonomous driving, and wireless control systems. Indeed, this is one of the services that is expected to be a source of value in 6G wireless networks.
Effective use of this computing infrastructure would involve efficient selection of the devices that will offload their tasks, and joint allocation of the computing resource at the network access point and the communication resources to and from the access point. The computing resource allocation is dependent on the number of operations required by the task and the capabilities of the infrastructure, while the communication resource allocations are dependent on the description length of the task and the outcome, the “state” of the communication channels, and the capabilities of each transmitter. These allocations are coupled by the deadline by which each device requires the outcome of its task. The degrees of freedom in these resource allocations are determined by the overall system framework.
This talk seeks to outline the key principles in framework selection and resource allocation in a scenario in which the goal is to minimize the cost of the energy expended by the devices. To emphasize the principles, the problem is decomposed into an outer problem that selects devices for offloading, an intermediate problem of computing resource allocation and an inner problem of communication resource allocation. By designing a framework that enables flexible communication resource allocation and developing efficient resource allocation algorithms, we gain insight that yields efficient computing resource allocation algorithms, and efficient algorithms for the selection of offloading devices.
The event will occur in the Information Technology Building (ITB), room ITB A113, at McMaster University in Hamilton, Ontario.
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4L7
Campus Map
ITB Location
McMaster parking map is available here. The closest parking lot is parking lot I which is next to the ITB building. A convenient and economical solution is to park on lot M which is a 10-minute walk from the ITB building (shuttle service is also available).
Kazem Cheshmi, Assistant Professor, Dept. of Electrical and Computer Engineering, McMaster University
Special thanks to our volunteers from the SwiftWare lab: Hossein Albakri, Samira Jamali, Da Ma, Mehdi Salehi, Nana Poku, and Yue Xu.
| Timings | Program |
|---|---|
| 9 - 9:20 | Welcome, coffee and refreshments, and opening remarks |
| 9:20 - 10 | Invited Talk 1: Prof. Tim Davidson, Multiple Access Computation Offloading |
| 10 - 10:20 | Contributed Talk 1: Dr. Conor McCoid, Accelerating fixed point iterations with Newton's method |
| 10:20 - 10:40 | Contributed Talk 2: Dr. Fauzia Jabeen, Approximating Second-Order Parametric Sensitivities in Moderately Stiff Stochastic Discrete Biochemical Models |
| 10:40 - 11:00 | Coffee Break |
| 11:00 - 11:40 | Invited Talk 2: Prof. Adam Stinchcombe, High Accuracy Computation for Electrical Impedance Tomography |
| 11:40 - 12:00 | Contributed Talk 3: Ms. Yasman Torabi, Blind Source Separation in Biomedical Signals Using Variational Methods |
| 12:00 - 12:20 | Contributed Talk 4: Mr. Mykhailo Briazkalo, Generating Realistic Financial Time Series with Ambient Diffusion Models |
| 12:20 - 1:40 | Lunch Break |
| 1:40 - 2:20 | Invited Talk 3: Mehran Ebrahimi, Constrained Shape Gradients in Level-Set Topology Optimization: Bridging Geometry and Design |
| 2:20 - 2:40 | Contributed Talk 5: Mr. Ray Wu, High-order Numerical PDE methods for Pricing Multi-asset Options on Sparse Grids |
| 2:40 - 3:00 | Contributed Talk 6: Mr. Da Ma, Sparsified Preconditioned Conjugate Gradient Solver on GPUs |
| 3:00 - 3:20 | Coffee Break |
| 3:20 - 3:40 | Contributed Talk 7: Prof. Spencer Smith, The Who, What, When, Where, Why and How of Scientific Software Verification Planning |
| 3:40 - 4:00 | Contributed Talk 8: Dr. Fabian Bleitner, Systematic Search of Extreme Behaviour in Fluid Dynamics via Energy-Based Blow-Up Criteria |
| 4:00 - 4:20 | Contributed Talk 9: Dr. Tristan Montoya, Entropy-stable discontinuous spectral-element methods for the shallow water equations on the sphere |
| 4:20 - 4:40 | Contributed Talk 10: Elkin Ramirez, Systematic search for extreme behavior in 3D Navier-Stokes flows based on the Ladyzhenskaya-Prodi-Serrin conditions |
| 4:40 - 5:00 | Contributed Talk 11: Mohammad Mahdi Salehi, Loop Fusion in Matrix Multiplications with Sparse Dependence |