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NE 591 Finite Element Analysis for Nuclear Engineering
Fall 2026

NE 591 Finite Element Analysis for Nuclear Engineering

3 Credit Hours

Wen Jiang

Asst Professor

This course provides a practical introduction to the finite element method as a numerical technique for solving linear ordinary and partial differential equations. Topics covered include Galerkin and weighted residual methods, principles of virtual work, discretization strategies, element formulation and evaluation, constitutive models, mixed formulations, and transient analysis. The course focuses on solving partial differential equations, with applications in heat conduction, linear elasticity, and advective-diffusive transport, covering a broad range of topics relevant to students of nuclear engineering. Emphasis is placed on the formulation and programming of finite element models, as well as the providing students with familiarity and hands on experience with finite element analysis software (MOOSE), which is the preferred platform for nuclear engineers.

Prerequisites

None.

Course Objectives

Upon completion of this course, students will be able to:

  • 1.Explain the fundamental concepts underlying the finite element method, including discretization, interpolation, and numerical approximation of governing equations.
  • 2.Derive the weak and variational forms of governing differential equations using the weighted residual and Galerkin methods.
  • 3.Formulate element stiffness matrices and force vectors for 1D and 2D problems in mechanics, heat conduction, and advective-diffusive system for nuclear engineering.
  • 4.Implement simple finite element programs in MATLAB/Python to solve linear problems and verify numerical convergence.
  • 5.Analyze FEM results, including accuracy, stability and convergence behavior.
  • 6.Use open-source finite element software MOOSE to model and analyze multiscale materials behaviors and multiphysics nuclear problems of nuclear engineering.
  • 7.Implement time-dependent and coupled equations (multiphysics) relevant to nuclear engineering.

Course Outline

This course consists of 10 topics:

  • I.Introduction and overview of finite element method
  • II.Integral forms and variational methods
  • III.One-dimensional boundary value problems
  • IV.Multidimensional problems, applications to steady state heat conduction and mechanical deformation in nuclear systems.
  • V.Element design and programming concepts
  • VI.Transient Analysis, Application to transient heat conduction in nuclear systems.
  • VII.Error analysis
  • VIII.Constrained media problems.
  • IX.Advective/diffusive systems, applications to fluid modeling in nuclear systems.
  • X.Introduction of the MOOSE framework

Textbook

Recommended textbook:
• Hughes,T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Publications.
Estimated cost of book at Amazon: new $40.

The lecture notes will be provide which cover the most important materials in the textbook above. Purchasing the textbook is high recommended but not required.

Software Requirements

Multiphysics Object-Oriented Simulation Environment: https://mooseframework.inl.gov

Created: 04/17/2026.