Tempus: Time Integration and Sensitivity Analysis Package

Introduction

Tempus is a software framework for the time integration of ordinary differential equations (ODEs), partial differential equations (PDEs), and differential-algebraic equations (DAEs). Examples of time-integration methods available are

• Forward Euler
• Backward Euler
• Explicit Runge-Kutta
• Diagonally Implicit Runge-Kutta methods
• Newmark-β
  • Explicit A-form
  • Implicit A-form
  • Implicit D-form
• Hilber-Hughes-Taylor (HHT-α)
• Implicit/Explicit Runge-Kutta (IMEX-RK) methods
• Partitioned IMEX-RK methods

Tempus provides a general infrastructure for the time evolution of solutions to ODEs, PDEs, and DAEs, through a variety of general integration schemes, and can be used from small systems of equations (e.g., single ODEs for the time evolution of plasticity models) to large-scale transient simulations requiring exascale computing (e.g., flow fields around reentry vehicles and magneto-hydrodynamics).