Structure-Oriented Paradigm Through Exact Complexes for Numerical Schemes

Explore a structure-oriented paradigm for developing numerical schemes through exact complexes in this conference talk from ICBS2025. Learn how exact complexes provide a mathematical framework for constructing numerical methods that preserve important structural properties of differential equations. Discover the theoretical foundations of this approach and understand how it can lead to more robust and accurate computational schemes. Examine specific applications where structure preservation is crucial for maintaining physical properties and mathematical consistency in numerical solutions. Gain insights into the advantages of this paradigm over traditional numerical methods and see how exact complexes can guide the design of next-generation computational algorithms for complex mathematical problems.