Spring 2026 Graduate Course - Advanced Numerical Methods Theory & Practice

Course Description

This course will enable students and researchers to understand and apply the theory behind numerical simulation, optimization of electrochemical engineering and other engineering models described by nonlinear differential, differential-algebraic, partial differential equations. The intent is to provide a self-contained, fundamental and practical approach to the theory, algorithm development and implementation relevant for electrochemical systems, and in particular batteries. Weekly lab modules will include application of the materials for models from mechanical, electrochemical, chemical, electrical, and energy systems (batteries and fuel cells). A distinguishing feature of this course is the training of graduate students with different backgrounds in theory and implementation of numerical methods for models that arise from multiscale-multidomain-multiphysics-multiphase modeling of electrochemical systems. The models solved involve some domain-specific challenges – nonlinearity and ill-conditioning resulting from Butler-Volmer kinetics, boundary layers, singularities, discontinuous transport properties across the interfaces, differential algebraic equations (DAEs) that cannot be solved with standard solvers (MATLAB’s ode15s, IDA). Knowledge of electrochemistry is not a requirement and the course will be based on models provided in ODE/PDE form with well-defined boundary conditions.

Instructor: Professor Venkat Subramanian, venkat.subramanian@utexas.edu