Benchmarks
Waveller2005 vs FEM solver
The following benchmark compares standard finite element method and Waveller2005 for a 3D acoustic Helmholtz problem in an unbounded domain. The FEM solution is computed using Femlab 3.1. Femlab uses 2nd order polynomial finite element method whereas Waveller software utilizes the ultra weak variational formulation and plane wave basis functions.
The problem consists of an ultrasound field which is emitted by a vibrating surface on a perfectly rigid baffle. The source is a 20 x 20 mm rectangular transducer which oscillates on a constant normal velocity amplitude. The dimensions of the computational domain in (x,y,z)-directions are 40 x 100 x 40 mm and the source is located at the y=0 plane at the end of the computational domain. All results are computed using a standard PC with 3 GHz Pentium 4 with 3 GB of RAM. Both solutions are compared with the numerical approximation of Rayleigh integral which is a semi-analytic solution of the problem.
Since both methods approximate the unbounded physical problem in a bounded computational domain, an additional error is induced by the use of an absorbing boundary condition (ABC) on the exterior boundary. The same low order (Sommerfeld-type) ABC is used with both methods since this is the only ABC readily available in Femlab. The accuracy of Waveller can be improved by using the perfectly matched layer (PML) method as the ABC.
Tables 1-3 list the element size h (given for Femlab's mesh generator), element number (Elem.), total CPU time, relative error compared to the Rayleigh integral and memory requirement (Mem.) as a function of frequency f. It is notable that all Waveller results are computed in a same mesh by increasing the number of the plane wave basis functions with the frequency. Table 3 shows the improved accuracy of Waveller when the PML is used.
| f (kHz) | h (mm) | Elem. | CPU time (s) | Error (%) | Mem (GB) |
| 100 | 3 | 101 978 | 448 | 30.88 | 1.4 |
| 150 | 1.8 | 478 471 | 4699 | 25.39 | 2.5 |
| 200 | 1.8 | 478 471 | 5321 | 20.64 | 2.5 |
| 300 | 1.8 | 478 471 | 5391 | 30.13 | 2.5 |
| f (kHz) | h (mm) | Elem. | CPU time (s) | Error (%) | Mem (GB) |
| 100 | 15 | 16 926 | 275 | 28.56 | 0.2 |
| 150 | 15 | 16 926 | 353 | 23.22 | 0.3 |
| 200 | 15 | 16 926 | 449 | 20.07 | 0.4 |
| 300 | 15 | 16 926 | 854 | 18.96 | 1.1 |
| f (kHz) | h (mm) | Elem. | CPU time (s) | Error (%) | Mem (GB) |
| 100 | 15 | 20 559 | 506 | 10.05 | 0.2 |
| 150 | 15 | 20 559 | 599 | 5.94 | 0.3 |
| 200 | 15 | 20 559 | 938 | 4.90 | 0.5 |
| 300 | 15 | 20 559 | 1272 | 3.39 | 1.1 |
Whats new
May 5th 2007
Waveller IPR have been acquired by Kuava ltd. Kuava continues Waveller development and uses it for simulation services.July 21th 2006
Waveller Acoustics 1.1 is available! Pricing information and information on how to receive an evaluation license are on page Waveller Acoustics.February 2nd 2006
Waveller ElectromagneticsThe first results using Waveller Electromagnetics are available in article Solving Maxwell's Equations Using the Ultra Weak Variational Formulation and in the screenshots-section. The mathematical formulation of Waveller Electomagnetics is extremely useful for solving electromagnetic field related wave problems in many application fields. We are currently seeking collaborators for developing a COMSOL plug-in for Waveller Electromagnetics.
