Depending on the problem at hand, other functions may be chosen instead of linear functions.Īnother benefit of the finite element method is that the theory is well developed. The coefficients are denoted by u 0 through u 7.īoth of these figures show that the selected linear basis functions include very limited support (nonzero only over a narrow interval) and overlap along the x-axis. ![]() The function u (solid blue line) is approximated with u h (dashed red line), which is a linear combination of linear basis functions ( ψ i is represented by the solid black lines). Take, for example, a function u that may be the dependent variable in a PDE (i.e., temperature, electric potential, pressure, etc.) The function u can be approximated by a function u h using linear combinations of basis functions according to the following expressions: The finite element method (FEM) is used to compute such approximations. The solution to the numerical model equations are, in turn, an approximation of the real solution to the PDEs. These discretization methods approximate the PDEs with numerical model equations, which can be solved using numerical methods. Instead, an approximation of the equations can be constructed, typically based upon different types of discretizations. For the vast majority of geometries and problems, these PDEs cannot be solved with analytical methods. ![]() The description of the laws of physics for space- and time-dependent problems are usually expressed in terms of partial differential equations (PDEs). ![]() Therefore reading a few books, and as you say do the exercicies, is the best way to learn COMSOl, in my viewPhysics, PDEs, and Numerical Modeling Finite Element Method An Introduction to the Finite Element Method And there are not many "simple" examples showing this, most COMSOl experts find it too trivial, but it remains for me essential for rapidly using COMSOl correctly andallowing the users to use the full power of the adopted conventions. This becomes acceptable for users with long experience in COMSOL, but it's very confusing the first time you take COMSOL in hand, as you have the specific notations to learn, the GUI interfaces, the physics logic used etc. questions like: when is "My_BC_V0" a parameter, a constant variable, a global variable a field of formally expression My_BC_V0(x,y,z,t). I found it very confusing to undertsand, in the eginning. You are right (and wrong) Dao, at least for me the books are more generic with more math and physics in a larger sense than most COMSOL examples.Īnd I'm missing an introduction to the maths conventions in COMSOL, that concentrate on the conventions and the link between conventional math writing and the COMSOL GUI entries, we are all used to write math more or less the same way, all around the world, COMSOL is rewriting the math interface (and unifying, finally, the physics ), you use the dx*dy*dz everywhere (almost) in math integration writing but you have by convention removed them from the writing in COMSOL. ![]() Pryor, PhDĪ COMSOL gallery book - should have been an online thumbnail gallery not a book.Īnother way is doing the small and basic example close to your domain to learn Comsol. There are some interesting entry level problems there, and it is a great book to teach others - and also to learn if you are starter in Comsol.ģ) Introduction to Computation and Modeling with Differential Equations Lennart EdsbergĤ) Multiphysics Modeling Using COMSOL®: A First Principle Approach Roger W. But, seems he is very busy these days.Ģ) An Introduction to Modeling of Transport Processes Ashim Datta and Vineet Rakesh, Cornell University, New York, USA He was once a very active member of the forum too. I just wished he would write another updated book with more examples in additions. You understand how comsol works and how you can push the boundaries. A bit outdated from the diagrams compared to Comsol 4, but yet the tricks are great. 1) Multiphysics Modeling With Finite Element Methods William B.
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