The method is based on world-leading mathematics research at KTH and Chalmers, together with didactic research at Stockholm University. Computation is the leading principle and music and visual art is part of the pedagogical concept.
By learning a few basic algorithms anyone can understand and carry out advances programming and physics simulations. Get started!
We present the Digital Math framework as the foundation for modern science based on constructive digital mathematical computation. The computed result (coefficient vector, FEM function, plot, etc.) is a mathematical theorem, and the mathematical Open Source code, here in the FEniCS framework, and computation is the mathematical proof. We can also derive additional constructive proofs from the FEniCS and FEM formulation, such as stability.
Based on the Digital Math framework and the FEniCS realization, we present our Direct FEM Simulation (DFS) methodology together with predictions of the most advanced benchmarks available, unlocking the grand challenge of turbulence and aerodynamics.
Digital Math represents digitalization of mathematics, society, industry and society in the form of automated and easily understandable computation of mathematical models in the Open Source FEniCS framework with world-leading performance and recognized at the highest level of science and industry together with an effective pedagogical concept with combined abstract theory and mathematical interactive programming in a cloud-HPC web-interface.
With our computational framework you can predict and understand the grand challenges of science and technology.
This site is the Digital Math research environment. Johan Jansson is also leading the commercial Open Source spin-off Icarus Digital Math, supported by IVA, KTH Innovation, Vinnova, etc. Any commercial activities will be denoted by "Icarus".
Johan Jansson (firstname.lastname@example.org), Massimiliano Leoni, Måns Andersson, Patricia Lopez Sanchez, Mats Stading, Ridgway Scott, Claes Johnson, Predictive Real Unified Continuum modeling of multi-physics in the Digital Math framework, Digital Math: Human workshop, 2020
Johan Jansson, Docent lecture "Digital Math", KTH, 2020
Johan Jansson et. al., Time-resolved adaptive direct fem simulation of high-lift aircraft configurations. Springer Brief: Numerical simulation of the aerodynamics of high-lift configurations, 2017.
Johan Hoffman, Johan Jansson, Claes Johnson, New Theory of Flight, Journal of Mathematical Fluid Mechanics, 2015
Johan Hoffman, Johan Jansson, Niclas Jansson, Rodrigo Vilela de Abreu, Claes Johnson, Computability and Adaptivity in CFD, Encyclopedia of Computational Mechanics, 2016
Johan Hoffman, Johan Jansson, Niclas Jansson, FEniCS-HPC: Automated predictive high-performance finite element computing with applications in aerodynamics, Lecture Notes in Computer Science, 2016
Johan Hoffman, Claes Johnson, Resolution of D'Alembert's paradox, Journal of Mathematical Fluid Mechanics, 2011
Johan Hoffman, Claes Johnson, Computational Turbulent Incompressible Flow, Springer, 2007
Claes Johnson, Johan Jansson, Secret of Flight Web Site, 2012- (older format)
Claes Johnson, Johan Jansson, Secret of Flight Web Site, 2020- (new format, to appear)
A. Logg, K.-A. Mardal, G. Wells, et. al., ``Automated solution of differential equations by the finite element method'', Lecture Notes in Computational Science and Engineering, 84 (2012), pp. 1-736. (2 chapters in ``the FEniCS book'')
Read more about our breakthrough predictive technology, take our courses, and meet our highly merited Team who are passionate about Digital Math.email@example.com
February 3, 2022
Our Vinnova project ELISE spearheading electric aviation highlighted as a success, where we have developed a paradigm-shift in predictive aerodynamics simulation in collaboration with e.g. NASA (https://lnkd.in/gnBcU5Qp) for robust and efficient certification and design. Now the Swedish government is planning a specific focus in this direction!
August 4, 2020
Many congratulations to Ezhilmathi Krishasamy ("Mathi") for publishing his PhD thesis, supervised by Johan Jansson.
Mathi is now continuing his academic career as a Post-Doc at the University of Luxembourg.
March 27, 2020
Digital Math will exhibit at the World Expo 2020 in Dubai with Vinnova!
The exhibition will be showcasing the DigiMat online education project supported by Vinnova, with example applications of predictive Real Flight Simulation of electric aircraft in the ELISE project: https://expo2020.se/
March 26, 2020
DigiMat is mathematics education for the digital world from basic school level : through top academic, professional level and teachers.
DigiMat is a unified program with varying depth and scope over all levels with computation as leading principle, where all mathematical objects are constructed by computation according to computer programs as mathematics expressed in symbolic form.
Try our prototypes and learn predictive Real Flight Simulation!
May 14, 2019
The report "Reproducibility and Replicability in Science" by the US National Academies of Sciences, Engineering and Medicine is just out, it's of key importance for our scientific work. Here's an article on the report, and the report itself:
Lorena Barba is a prominent US scientist, driving forward several Open Source initiatives such as NumFOCUS, and one of the authors of the report.
Here's a quote from the article:
Barba told Physics World. “What we are calling for is changing those norms to give importance to the full set of digital objects that are part of a scientific study and acknowledging that the scientific paper is insufficient today in its methods section to include all of the information needed for another researcher to confirm the results or build from those results.”
What Lorena is saying is that if a scientific paper is not reproducible, then it cannot really be considered a scientific publication. Here's another article on this:
This is also mirrored in the Swedish guidelines for Open Access in Science:
There is a crisis of reproducibility in science today:
One of the most cited papers in recent years is the paper "Why most published research findings are false":
The Digital Math framework as the foundation for modern science based on constructive digital mathematical computation, is a solution to the crisis. The computed result (coefficient vector, FEM function, plot, etc.) is a mathematical theorem, and the mathematical Open Source code, here in the FEniCS framework, and computation is the mathematical proof.
Based on the Digital Math framework and the Unicorn/FEniCS realization, we present our Direct FEM Simulation (DFS) methodology together with predictions of the most advanced benchmarks available, unlocking the grand challenge of turbulence and aerodybamics.