Mathematical, Computational, & Engineering Physics

Usage Requirements: Internet Connection

Wolfram Alpha is an online calculator that is capable of easily converting between units, numerical calculations using fundamental constants, and doing calculations that are more advanced than other online calculators, such as solving systems of equations, matrix manipulation, and solving differential equations.

Contributor: Ricky Dube, Indiana University - Bloomington

Ansys is a company which provides analytical tools for modeling physical phenomena in mechanical systems. They provide products for analyzing fulid mechanics (Ansys Fluent), 3D design (Ansys Discover), structural mechanics (Ansys Mechanical), thermal load in electronics (Ansys Icepak), electromagnetic fields (Ansys HFSS), optics (Ansys Zemax OpticStudio), and more. There are also simulation options to assist in product design.

Contributor: Amelia Binau on behalf of Brenna McConnell, Indiana University - Bloomington

Language Requirement(s): Variable (software only) - C, Fortran, Python, and more. Usage Requirements: Internet connection for general catalog, relevant compiler for software.

It's in the name! NIST Digital Library of Mathematical Functions is a simple, yet well-updated, website from the American National Institute of Standards and Technology (NIST) features a catalog of mathematical functions, many of which are heavily relevant to physics. An online companion NIST Handbook of Mathematical Functions. It also contains a helpful guide to available mathematical software for different applications, many of which are open-source and require languages such as C, Fortran, or Python.

Contributor: Amelia Binau, Indiana University - Bloomington

Usage Requirements: Requires C++ and Linux (Native) or WSL for Windows/MacOS. Relies heavily on MPI for parallel processing. Scales from multi-core laptops to massive supercomputers. Processes case directories containing custom syntax plaintext dictionaries (e.g., controlDict). Works offline.

A premier, industry-standard, open-source toolbox for Computational Fluid Dynamics (CFD). Users configure mesh, physics, and boundary conditions via structured text files to simulate complex fluid flows, heat transfer, and chemical reactions, flattening the financial barrier for researchers conduction advanced fluid analysis.

Contributor: Neil Ghugare, University of Florida, The Ohio State University

Language Requirement(s): MATLAB. Usage Requirements: MATLAB environment.

Chebfun is a MATLAB package created in 2002 that allows the user to work with and visualize a plethora of advanced mathematical functions. It serves as the primary tool for examples in the textbook Approximation Theory and Approximation Practice, of which example codes and the first 6 chapters are available online. Work with linear and nonlinear ODEs, integration methods, Chebyshev expansions, complex analysis, Fourier analysis, PDEs, multivariate approximation methods, and more. Chebfun is well-documented, featuring a guide which includes its extensions Diskfun and Spherefun. Must be awfully fun!

Contributor: Amelia Binau, Indiana University - Bloomington

Language Requirement(s): Python. Usage Requirements: Python-compatible IDE.

Need more precision in your calculations than base Python offers? mpmath allows the user to carry out calculations, whether real or complex, to an arbitrary decimal precision and also includes a robust library of special functions. With co-implementation of gmpy2, users may arithmetically manipulate data at precisions over 100 decimal points. This package is integrated into popular packages/systems such as Sage and SymPy.

Contributor: Amelia Binau, Indiana University - Bloomington

Language Requirement(s): Python or C++ interface. Backend components rely on C++. Usage Requirements: Works natively with MacOS or Linux, Windows requires WSL or Docker. Integrates with MPI for parallel computing if required.

FEniCS is an open-source package for solving partial differential equations (PDEs), specifically using the finite element method (FEM). It has high-level Python and C++ interfaces, and runs on a wide range of hardware, from standard laptops to supercomputers. Some examples of usage within the physics/engineering world include solving: the heat equation, multiple styles of Poisson equations, linear elasticity and hyperelasticity equations, Navier-Stokes equations, and the Helmholtz equation. Additionally, the FEniCS project provides a free ebook that explains the theoretical background and design of FEniCS, and showcases applications. It is important to note that the book hasn't been updated since 2012, so while the theoretical framework is valid, the code examples may be out of date.

Contributor: Neil Ghugare, University of Florida

Language Requirement(s): Python, C++, and/or Scheme API. Usage Requirements: Runs on Linux or MacOS. Supports multi-core scaling via MPI. Relies on LAPACK/BLAS for linear algebra tools. Works offline. Outputs HDF5 files.

Meep is an open-source package for the simulation of electromagnetics using the finite-difference time-domain (FDTD) method. It is completely scriptable via Python, C++, or Scheme APIs, and allows for simulations in one to three dimensions, and even in cylindrical coordinates. It contains many features for electromagnetic simulations, including but not limited to: arbitrary material types, a materials library, multiple boundary conditions, differing symmetries, wave solvers, and field analysis tools like Fourier transforms and Poynting flux analysis.

Contributor: Neil Ghugare, University of Florida

Language Requirement(s): The core engine is in C++, but a user can interface with it in Python, C++, MATLAB, and/or Fortran. Usage Requirements: Works on Linux, MacOS, or Windows. It can integrate with standard packages, like NumPy's standard numerical arrays. Works offline.

Cantera is an open-source package that helps solve problems in chemical kinetics, transport processes, and thermodynamics. It allows for engineering physicists to model complex physical phenomena. This includes reactive fluid dynamics, electrochemical battery reactions, plasma chemistry, and combustion mechanics. It does so by solving ordinary differential equations (ODEs) and state equations.

Contributor: Neil Ghugare, University of Florida

Language Requirement(s): Written in C, but has interfaces for Python or Fortran. Usage Requirements: Installed via Spack or CMake. Can be built with MPI support or GPU acceleration. Works offline across Linux, MacOS, and Windows.

SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers) is an open-source library developed by LLNL that helps solve mathematical equations of physical phenomena. It can be easily incorporated into existing simulation codes, consisting of six packages, including: ordinary differential equation (ODE) systems, differential-algebraic equation (DAE) systems, and nonlinear, algebraic systems.

Contributor: Neil Ghugare, University of Florida

Language Requirement(s): Python 3.10+ managed via pip or uv. Usage Requirements: Runnable directly via local scripts, works offline in that form.

HEACalculator is a Python package for calculating phenomenological parameters for High Entropy Alloys (HEAs). It uses thermodynamics and physics to predict the formation of solid solutions for HEAs. It can predict and calculate multiple utilities, like valence electron concentration (VEC), mixing enthalpy \(\Delta H_{\rm mix}\) and entropy \(\Delta S_{\rm mix}\), and atomic size differences \(\delta\), among others.

Contributor: Amelia Binau, Indiana University - Bloomington, Curator; Neil Ghugare, University of Florida, Writer

Language Requirement(s): Variable. Usage Requirements: Familiarity with Kaggle (tutorials available).

Need data for ML analysis of fluid dynamics? BLASTNet is a project designed to compile open-source datasets on hydrodynamic systems for training machine learning algorithms. BLASTNet's website contains tutorials for accessing data through Kaggle (where most of its content is stored) and training ML's. Study homogeneous isotropic turbulence, shocks, channeled flow, jet fuel flows, and even propagation of wildfires. Added plus, most datasets are well-introduced with a summary of theoretical background in BLASTNet's catalog.

Contributor: Amelia Binau, Indiana University - Bloomington