On this page we present a list of independent consultants capable of developing FlexPDE models for various applications.

(These consultants are not employees of PDE Solutions. We make no attempt to evaluate them, and take no part or responsibility in any relationship established between consultants and clients.)

If you are a FlexPDE user and wish to be listed as a FlexPDE consultant, give us a brief statement of interests and a link to your website or your Email address, and we will include your link here.

Dr. Mike Moore
AetherMachines Inc.

My simulation experience prior to the use of FlexPDE was rotational mechanics and thermodynamics using Easy5x formerly from Boeing, as well as hardware in the loop state space turbine control system simulation and torpedo simulations. I have always wanted to augment some of this process/hardware simulation with more of a partial differential equation approach (as opposed to the cascade first order responses found in most real time/state space simulations) and FlexPDE is the perfect tool for such.

Currently, I use FlexPDE to augment the above systems, controls, and SPICE circuit simulations to provide detailed models of thermodynamics, electrostatics, and to some extent fluid subsystem responses in designs. For example, a heat sink or fluid heat transfer problem may be need to be accurately characterized to properly sweep temperature in a SPICE or control system simulation, and hence FlexPDE fits right in.

In addition to the ‘pure numerics’ of FlexPDE, I also use Mathematica to validate and simulate the analytic assumptions and modeling constructs behind such systems, controls, and circuits for which FlexPDE gives the PDE modeling.

Craig Nelson
Phone: (206) 498-9447

I am a research engineer with many years experience solving difficult technical problems, both at the workbench and using numerical methods.  I have used FlexPDE intensively for eight years and have produced well over a hundred models, some resulting in complex multi-physics full-field solutions.  Here is a partial listing of my work:

fluid dynamic electrochemical fuel cell electrodes;  electromagnetic wave propagation in partially filled waveguides; acoustic wave propagation in solids and liquids;  stress and deflection in piezo-pump diaphragms;  two-phase fluid flow in fluidic channels;  magnetic levitation forces on moving magnets;  toothbrush induced fluid shear flow over teeth;  gas-evolving chemical reactions in a micro-reactor;  various fuel cell micro-fluidic situations;  vibrational modes of complex ultrasound transducers;  various heat flow situations;  electric current flow in patterned thin film conductors;  electric fields in various capacitve transducers;  self focussing of a high intensity gaussian beam;  self-convection of heated fluids;  stress build-up in cooling adhesive bonds;  tidal flow in a Mexican river estuary; pressure deflection of clamped thick plates;   forces on a rising bubble;  fluidic resistance of channel blockages; electro-magnetic wave propagation in doped porous silicon wafers.

I have a relatively well equipped acoustics, electronics, optics and microwave lab for determining and confirming numerical model parameters and am willing to travel to teach individuals and small groups the ins-and-outs of FEA, as practiced using FlexPDE.

Dr. Gunnar Backstrom
Consultant - Use of FEA in Undergraduate Education

I have written several books on the use of finite-element analysis for undergraduate education. This is a completely new tool for understanding the theory of fields, so far little exploited in universities. My books are described in detail on my web page,

I am ready to discuss such application with anyone who is curious but not yet completely convinced.

Dr. Víctor H. Cortínez
Associate Professor and Scientific Research Director,
Grupo de Análisis de Sistemas Mecánicos, Universidad Tecnológica Nacional (FRBB).

Areas of interest: Structural Mechanics and Fluid Mechanics.

He has authored over 50 journal papers on structural mechanics (in Journal of Sound and Vibration, Structural Engineering and Mechanics, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Applied Acoustics, etc.)

Bill Jones
Consultant - System Modeling and Underlying Physical Science for Product Development, since 1983.
Phone:  (954) 772-9567
Email:  or

My history is mostly that of internal consultant in physical science and mathematical modeling.  A partial list: of products includes:

  • Fishfinder (SONAR) transducers  (modeling to identify superfluous expense)
  • Blood cell counters (modeling several aspects, from materials behavior to  cell behavior, see US patent #5452237)
  • Device behavior (3-d) of various subcomponents (MOSFETs, BJTs, others) of   several integrated circuit technologies, usually toward refining SPICE  models.
  • Stress limits in plastics (press-fit assemblies)

Most projects have been for startups later bought by such companies as Abbott Laboratories, Allied/Bendix, Schering-Plough, DataLinear (became Sipex) and Raytheon.

I've used FlexPDE to model heat transfer, acoustic behavior of materials and structues and fluid flow (water) around boat hulls.

I'm interested in finding a group of companies that need modeling capability but don't want to hire a fulltime person to do it. You can be in any geographic area, but I don't travel on a regular basis.  A visit is fine, but we should do most work over the internet.  If your operation is in South Florida within about 50 miles of Fort Lauderdale, even better.  In particular, if you have a marine application

Dr. Hermann Klocker.

Thesis 1991 and Ph. D. 1998 for works on the usage of the Finite-Element-Method ( Areas of interest and experience in the fields of heat transfer and thermo-elastic problems (many studies for PLANSEE AG( My specialized field of knowledge is the usage of analytical or semianalytical methods in combination with the efficient usage of Finite-Element-Methods.

Contact: Hermann Klocker, Gymnasiumstrasse 5/5, A-6600 Reutte, Austria.

Dr. Geoff Mercer
Senior lecturer in Applied Mathematics
School of Physical, Environmental and Mathematical Sciences
University of New South Wales
at the Australian Defence Force Academy
Canberra, Australia


Recent use of FlexPDE in heat and mass transfer problems including
- skin burns
- combustion waves
- pesticide uptake in plant leaves
- flow through and over porous shelterbelts
- wool scouring

I am available for consultancy work but am more
interested in collaborative research projects with
mutual beneficial results.