Infinite Elements, Perfectly Matched Layers, and Absorbing Layers
Simulation of Infinite Domains
Simulation of unbounded or infinite domains is a challenge encountered in many types of physics. Normally, any physics simulates a process within a bounded domain represented by the geometry drawn in, or imported into, COMSOL Multiphysics. But the domain is often delimited by artificial boundaries inserted to limit the extent of the model to a manageable region of interest. You might not be interested in the details of the solution far away from any sources, loads, or material inhomogeneities, but the solution inside the region of interest must not be affected by the presence of the artificial boundaries. You simply want it to behave as if the domain was of infinite extent. In general, for field problems, unless the boundaries of the simulated device correspond to well-defined boundary conditions (such as a constant electric potential), then you need to include sufficient surrounding volume, so that the external boundaries of the computational space can be specified in a way that does not interfere with computations of the correct fields in or on the device that you are modeling.
Artificial truncation of the domain can be handled in several ways. Some physics interfaces include special boundary conditions to absorb outgoing propagating waves without spurious reflections, so-called low-reflecting boundary conditions. Others allow impedance boundary conditions, which can account for a finite impedance between the model boundary and a reference at infinity. Such boundary conditions are often efficient and useful but lack some generality and sometimes accuracy.
Another way to accomplish the same desired effect is to apply a coordinate scaling to a layer of virtual domains surrounding the physical region of interest. For stationary and transient problems, these virtual domains can be stretched out toward infinity, giving rise to infinite elements. To absorb outgoing waves in a frequency-domain problem, you must instead stretch the virtual domains into the complex plane, creating so-called perfectly matched layers (PMLs). In addition, for transient problems using a time-explicit solver, you can add an absorbing layer, which acts like an effective nonreflecting-like boundary conditions.
The Infinite Element Domain, Perfectly Matched Layer, and Absorbing Layer nodes are only available with the following add-on products for applicable physics interfaces:
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Infinite Element Domain: AC/DC Module, Structural Mechanics Module, MEMS Module, Heat Transfer Module, Chemical Reaction Engineering Module, Subsurface Flow Module, Batteries & Fuel Cells Module, Electrodeposition Module, Corrosion Module, Electrochemistry Module, and Plasma Module.
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Perfectly Matched Layer: Acoustics Module, RF Module, Wave Optics Module, Structural Mechanics Module, and MEMS Module,
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Absorbing Layer: Acoustics Module, RF Module, and Wave Optics Module
Because of their common background as coordinate stretching, infinite elements and PMLs in COMSOL Multiphysics share a number of important properties. They share part of the user interface and many modeling principles can be translated directly from one to the other. In the description below, infinite elements and PMLs are therefore sometimes referred to collectively as scaling systems.
The Scaling System node provides direct access to coordinate transformation machinery underlying PMLs and infinite elements.