In this work, we present a non-overlapping substructured DDM with PML transmission conditions for checkerboard (Cartesian) decompositions that takes cross-points into account. Unfortunately, the extension of the PML-based DDM for more general partitions with cross-points (where more than two subdomains meet) is rather tricky and requires some care. They are shown to be a good compromise between basic impedance conditions, which can lead to slow convergence, and computational expensive conditions based on the exact Dirichlet-to-Neumann (DtN) map related to the complementary of the subdomain. Transmission operators based on perfectly matched layers (PMLs) have proved to be well-suited for configurations with layered domain partitions. ![]() It is well-known that the convergence rate of non-overlapping domain decomposition methods (DDMs) applied to the parallel finite-element solution of large-scale time-harmonic wave problems strongly depends on the transmission condition enforced at the interfaces between the subdomains. Those computations show a reduction of 46% in the iteration count, when comparing an operator optimized for cavities with those optimized for unbounded problems. In particular, computations of the acoustic noise in a three-dimensional model of the helium vessel of a beamline cryostat with optimized Schwarz schemes are discussed. Nonetheless, deviations from this ideal geometry are considered as well. Notably, this paper focuses on the case of rectangular cavities, as the optimal (non-local) transmission operator can be easily determined. This work explores new operators taking into account those back-propagating waves and compares them with well-established operators neglecting these contributions. Such problems are heavily impacted by back-propagating waves which are often neglected when devising optimized transmission operators for the Schwarz method. closed domains which do not feature an outgoing wave condition). ![]() With some keywords, in this case it is lines.In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. If the version is 3.0 or higher, this pop-up window will appear.įor quadrilateral elements, 7 columns would be used, since eachĬells is a dictionary and allows to store information associated Geuzaine, Christophe, y Jean-François Remacle (2017), Gmsh Official International Journal for Numerical Methods in Engineering, Geuzaine, Christophe, y Jean-François Remacle (2009), Gmsh: A 3-Dįinite element mesh generator with built-in pre-and post-processingįacilities. Strength of Intact Rock Core Specimens, ASTM Now, let’s discuss the different parts of the code to see what it doesĪSTM D3967–16 (2016), Standard Test Method for Splitting Tensile savetxt ( "mater.txt", mater_array, fmt = " %.6f " ) savetxt ( "eles.txt", els_array, fmt = " %d " ) np. array (, ]) maters = cell_data els_array = # Create files np. flatten () nodes_array = - 1 nodes_array = - 1 # Materials mater_array = np. flatten () nodes_inf = lines nodes_inf = nodes_inf. zeros (( nloads, 3 )) loads_array = id_cargas loads_array = 0 loads_array = load # Boundary conditions id_izq = 1 ] id_inf = 2 ] nodes_izq = lines nodes_izq = nodes_izq. shape ) nodes_array = points # Boundaries lines = cells bounds = cell_data nbounds = len ( bounds ) # Loads id_cargas = cells nloads = len ( id_cargas ) load = - 10e8 # N/m loads_array = np. ![]() ![]() zeros (, 5 ]) nodes_array = range ( points. shape ) els_array = 3 els_array = eles # Nodes nodes_array = np. zeros (, 6 ], dtype = int ) els_array = range ( eles. cell_data # Element data eles = cells els_array = np. read ( "Prueba_brasilera.msh" ) points = mesh. Import meshio import numpy as np mesh = meshio.
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