Speaker
Description
The Generalized Truncated Power Series Algebra (GTPSA) is a high-order differential algebra framework that provides real and complex multivariate Taylor expansions with accuracy close to symbolic computation. It naturally supports automatic differentiation of abritrary order, with simultaneous propagation of mixed partial derivatives and functional composition, while maintaining high computational efficiency. GTPSA is among the fastest open-source libraries available for high-order differential algebraic computations.
In the field of accelerator physics, GTPSA forms the computational core of MAD-NG (Methodical Accelerator Design – Next Generation), a modern standalone framework for linear and nonlinear optics, as well as high-order beam dynamics analysis. Within MAD-NG, GTPSA enables direct computation of optical functions, linear and nonlinear lattice maps, and Lie algebraic operators with machine precision and full parametric dependency on user-defined expressions. Combined with the LuaJIT high-performance scripting engine and the C++ template-based parametric polymorphism, this architecture delivers exceptional computational throughput while preserving algebraic clarity and consistency.
This presentation will introduce the GTPSA formalism, its automatic differentiation mechanisms, and illustrate its application to advanced beam optics and nonlinear map analysis in MAD-NG, highlighting how high-order AD enables accurate and scalable modeling of modern accelerator systems.