In 1993, Bruaset received his PhD from the University of Oslo for work on preconditioners for Krylov subspace methods. He joined SINTEF Applied Mathematics shortly thereafter, where he together with Dr. Hans Petter Langtangen was a principal developer of Diffpack, a pioneering object-oriented software framework for numerical solution of partial differential equations. In 1997, he co-founded the company Numerical Objects AS, for the purpose of commercializing the Diffpack software framework. In Numerical Objects, Bruaset held the position as Vice President of Development, and has through close customer contact been exposed to a wide variety of industrial applications. Bruaset returned to research in 2003, when he joined the Simula Research Laboratory.
Since 1999, Bruaset has held a part-time position as Professor at the Department of Informatics, University of Oslo.
At Simula, Bruaset has headed the project Software for PDEs within the Scientific Computing Department. Since 2005, he has been responsible for building up a comprehensive, long-term research collaboration in Computational Geosciences between Simula and Statoil (formerly Hydro). This collaboration addresses important research problems in the industry, primarily related to oil and gas exploration. Statoil is one the world's largest crude oil and gas suppliers, and widely recognized as a company that pushes the technological frontiers.
In the period from October 2007 to September 2009, Bruaset combined the leadership and build-up of Simula's Computational Geosciences group with the position of Assistant Director at the Simula School of Research and Innovation AS. From September 2009 to June 2010, he held the position as Director of Research Applications, thereby leading Simula's efforts in technology transfer. From October 2009, he is Director of Research Education, which includes the management of the Simula School of Research and Innovation AS. He is still involved in the work and strategy of the Computational Geosciences group.
Bruaset has authored one book and edited four others.