Numerical Methods & Computational Simulation

The numerics underneath every FEA and solver run: linear algebra, root-finding and optimization, integration, differential equations, discretization error and stability.

Private cohorts & on-site
Format: 3-day (8:30 a.m.–4:30 p.m.)
Level: Intermediate
Location: Scheduled on demand · on-site at your facility or a regional venue
Date(s): Not yet scheduled for open enrollment. Get notified when it is, or book it privately for your team.
Includes: Certificate of Completion · printed slide binder · take-home reference text

Get notified when this course is scheduled

One email when dates are set. Or skip the wait: run it as a private cohort, on-site at your plant.

Talk to us about a private cohort
  • One email, no sequence
  • Never shared
  • Reply within one business day

Faculty

Faculty details for this seminar will be announced with the full schedule.

Fees

Early: $1,895 (payment 4+ weeks ahead)
Standard: $2,095 (check/ACH) · $2,165 (card)

Group discount: $200 off per attendee for 3+ from the same organization.

Also Available

  • Corporate on-site delivery at your facility
  • Private cohort sessions
  • Digital curriculum licensing

Seminar Overview

Every FEA run, solver call, and optimization your engineers trust depends on numerical methods — and those methods have failure modes. Built from MIT OpenCourseWare's numerical-analysis and computational-science curriculum, this seminar gives engineers the numerics underneath the tools: linear algebra, root-finding and optimization, numerical integration, differential equations, discretization error and stability. The payoff is engineers who can trust, audit, and diagnose simulation output instead of treating the solver as a black box — the difference between a number and a correct answer.

Ideal Learner

  • CAE, FEA, and CFD engineers who run and interpret solvers
  • Simulation and digital-twin engineers building computational models
  • Structural and dynamics engineers validating numerical results
  • Materials scientists using numerical models of behavior
  • Engineers reconstructing or auditing simulations for review

Learning Objectives

  • Explain how solvers discretize and solve engineering equations
  • Recognize and control error, instability, and convergence failure
  • Select numerical methods matched to the physics and required accuracy
  • Validate numerical results with convergence and residual checks
  • Audit a simulation and defend its numerical integrity

Consulting Sessions

Seminar attendees can sign up for individual consulting sessions with the instructor. Sessions are free for registered attendees, first-come first-served — sign up when registering by calling 248-539-0473 or during the seminar.

Seminar Outline

  • Direct vs. iterative linear solvers
  • Condition numbers and ill-conditioning
  • Why small numerical error can wreck a result
  • Bisection, Newton, and gradient methods
  • Local vs. global optimization
  • Pitfalls and the cost of convergence
  • Quadrature and its error
  • Finite-difference derivatives and accuracy
  • Sensitivity computation done right
  • ODE and PDE discretization (FD/FE), time-stepping
  • Stability, stiffness, and solver selection
  • Boundary and initial condition influence
  • Truncation vs. round-off error, convergence order
  • Grid/convergence studies and residual checks
  • Validating numerical models against physics and test
  • Auditing a solver setup for credibility
  • When simulation lies and how to catch it
  • Presenting numerical evidence for design review
  • Attendees run a convergence study on a representative problem
  • Diagnose error and refine the method
  • Produce a defensible numerical result

More in Track G — Computational & Quantitative Engineering

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