I am a researcher in the Applied Numerical Algorithms Group in CRD. I focus on scalable numerical and mathematical algorithms applied to problems where the accuracy of dynamics and multi-scale interactions are important.
I have also spent 12 years in IT consulting and architecture in startups and the financial services industry, which included roles in strategic planning, vendor management, software project leadership, business process and data analytics. I have a Ph.D. in Mechanical Engineering from the University of California, Berkeley.
See my LinkedIn profile for more information.
Current research projects and collaborations:
- Global atmospheric dynamics simulations. Developing a Chombo-based time-accurate, adaptive mesh refinement (AMR) dynamical core on the cubed sphere, with appropriate treatment of acoustic waves. See our recent conference poster.
- Multi-scale modeling combined with optimizaiton of urban energy usage. Developing a proof of concept for combined weather and energy simulation and optimization across different scales.
- Higher-order Finite Volume methods. Under DoE ASCR Applied Math program, developing scalable higher-order methods for complex PDE's. Examples include 4th-order adaptive methods for advection-diffusion, higher-order Embedded Boundary methods, and adaptive mapped multi-block discretizations.
- Embedded Boundary methods. Ongoing research into "cut-cell" approaches to PDE's ising EB Chombo, and the mathematical theory avoiding issues with "small cells," with applications to complex geometries and multi-material problems.
Ongoing research interests:
- Scientific software and evolving HPC architectures. The future of HPC platforms may be GPU/manycore systems, globally distributed cloud-type computing, or both. Coming up with approaches, algorithms and libraries that can solve bigger problems faster is an ongoing challenge. Work supported by DoE ASCR and an NSF SI2 project.
- Software Architecture in Scientiific Computing. My background as a systems and software architect in commercial settings contrasts dramatically with how things are done in most scientific computing teams, so I'm developing approaches to bridge those two worlds.
Q. Zhang, H. Johansen and P. Colella, "A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation", SIAM Journal on Scientific Computing, Vol. 34, No. 2. (2012), B179, doi:10.1137/110820105, 2010,
- Download File: O4AdvDiff.pdf (pdf: 599 KB)
McCorquodale, P., Colella, P., Johansen, H., "A Cartesian Grid Embedded Boundary Method for the Heat Equation on Irregular Domains", J. Comput. Phys. Vol.173 (2001), pp. 620-635, 2001,
- Download File: A148.pdf (pdf: 652 KB)
Johansen, H., Colella, P., "A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains", J. Comput. Physics, Vol.147, No.1, pp. 60-85, November 1998,
- Download File: A135.pdf (pdf: 390 KB)
Cartesian Grid Embedded Boundary Finite Difference Methods for Elliptic and Parabolic Partial Differential Equations on Irregular Domains, Johansen, H., 1997,
- Download File: HansJohansenThesis1997.pdf (pdf: 8.8 MB)