Electromagnetism is a fundamental branch of physics and a key component of many natural and engineered systems. Since its inception, electromagnetism has been a rich source of fundamental mathematical problems, especially in the theory and numerical computation of solutions to partial differential equations. In the past several decades, much research effort has been focused on phenomena arising from the interaction of electromagnetic fields, such as light, and underlying optical media, such as plasmas, glass fibers, gasses or crystals composed of active atoms, or artificial composites containing materials with different response properties. Analytical, asymptotic, and computational methods developed by applied mathematicians have proven to be important for investigating and understanding these phenomena.

Researchers at Rensselaer are investigating fundamental problems in electromagnetic wave propagation using these three classes of techniques, while at the same time further developing the mathematical tools. They have contributed to fields ranging from exactly solvable nonlinear partial differential equations used in optical pulse propagation, modeling of electromagnetic responses of composite materials and ionized plasmas, to highly accurate computational algorithms. These algorithms are designed to preserve important features of the underlying physical systems which for example enable accurate simulations of the problems and even of their long-time asymptotic behavior. These computational tools can be deployed on some of the largest computers in the world in order to help describe basic questions relating to electromagnetic phenomena.

Faculty Researchers:

• Donald Schwendeman
• Fengyan Li
• Jeffrey Banks
• William Henshaw