# A Computational Platform for Automatic Signal Processing for Bender Element Sensors +
## 3 Description of the GeoHyTE Platform
### Computational Architecture
#### 3.2.4 Algorithmic and Material Parameters  
The layout of GUI 2 is presented in Figure 4. The algorithmic parameters include the refinements of the time and space bases, the type of mesh generator to be used, and some options that control the execution of the finite element analysis. The definition of the Daubechies wavelet bases for the approximation of the time variation of the unknown fields requires the specification of the family number, the order of refinement, and the number of dyadic time points for the computation of the solution. The number of dyadic points \((d)\) controls the resolution of the time-history solutions, which are plotted in \(2^{d}+1\) equally spaced time points between zero and the total time of the analysis, which is also specified in the _Time integration_ zone of GUI 1. As shown in Section 3.1.2, hybrid-Trefftz elements use dual approximation bases in the domain and on the essential (kinematic, elastic, absorbing) boundaries. The domain approximation, constrained to satisfy all domain equations but none of the boundary conditions, consists of Bessel functions in the radial direction and exponential functions in the tangential direction, expressed in a local referential centred in the barycentre of each finite element. Order \(n_{D}\) of the domain basis should be input in the _Loops order_ field. The boundary bases are used to enforce the boundary conditions on the functions contained  
Figure 4: Layout of GUI 2.  
in the domain bases. They are built on complete Chebyshev polynomials, expressed in a boundary local referential. Order \(n_{\Gamma}\) of the boundary bases is input in the _Edge order_ field. Hybrid-Trefftz elements support distinct definitions of the orders of domain and boundary bases in different elements and essential boundaries, respectively. However, for simplicity, the GeoHyTE default is to use the same orders in all elements and essential boundaries. Advanced users can easily define distinct orders programmatically. To observe the kinematic indeterminacy condition, the total number of functions contained in all domain bases must be larger than the total number of functions contained in the boundary bases. While the compliance with this condition in the limit may be cumbersome to secure, its loose compliance is always ensured by using domain and boundary orders such that  
\[n_{D}\geq 2(n_{\Gamma}+1) \tag{6}\]  
The geomechanical properties of the material consistent with [PERSON]'s theory [29] must be specified in the _Material properties_ zone. The definition of some of these properties may be challenging for analysts less acquainted with [PERSON]'s theory. To support GeoHyTE's users in such situations, a short description of the involved parameters and the expressions used to compute them are given in Appendix A. The algorithmic parameters that need to be defined in GUI 2 are the number of Gauss quadrature points, the number of plotting points, the options to solve the spectral problems in parallel and to use iterative solvers for the algebraic system, and the type of the mesh generator. The Gauss quadrature points are used for the (boundary) integrations required to construct the finite element system. Insufficient Gauss points may lead to large errors in the coefficients, while an excessive number of points increase the computational time. The number of plotting points controls the resolution of the solution representation in each finite element. The total number of points where the solution is plotted inside each element is equal to the number of plotting points squared. The _Parallel processing_ option triggers the distribution of the time-discretised problems to be solved by all cores of the machine. The option requires the Parallel Processing Toolbox, but drastically increases the efficiency of the execution. Matlab's advanced users can control the number of cores that perform the calculations programmatically. The _Use least norm solvers_ option enables GeoHyTE to use least norm solvers on ill-conditioned solving systems.