scholarly journals The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1968
Author(s):  
Giovanni Aiello ◽  
Salvatore Alfonzetti ◽  
Santi Agatino Rizzo ◽  
Nunzio Salerno
Keyword(s):  
Integral Equation ◽  
Eddy Currents ◽  
Computing Time ◽  
Low Frequency ◽  
Dirichlet Condition ◽  
Open Boundary ◽  
Coordinate Transformations ◽  
External Layer ◽  
Electromagnetic Problems ◽  
Electrostatic Fields

This paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an unknown Dirichlet condition on the truncation boundary. An integral equation is used to express this boundary condition in which the integration surface is selected in the middle of the most external layer of finite elements, very close to the truncation boundary, so that the integral equation becomes quasi-singular. The method is described for the computation of electrostatic fields in 3D and of eddy currents in 2D, but it is also applicable to the solution of other kinds of electromagnetic problems. Comparisons are made with other methods, concluding that FEM-DBCI is competitive with the well-known FEM-BEM and coordinate transformations for what concerns accuracy and computing time.

scholarly journals Solution of skin-effect problems by means of the hybrid SDBCI method

2014 ◽  
Vol 33 (6) ◽  
pp. 1935-1949 ◽  
Author(s):  
Giovanni Aiello ◽  
Salvatore Alfonzetti ◽  
Nunzio Salerno
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Skin Effect ◽  
Singular Integrals ◽  
Computing Time ◽  
Dirichlet Condition ◽  
Open Boundary ◽  
Content Type ◽  
Hybrid Finite Element Method ◽  
Element Method

Purpose – The purpose of this paper is to present a modified version of the hybrid Finite Element Method-Dirichlet Boundary Condition Iteration method for the solution of open-boundary skin effect problems. Design/methodology/approach – The modification consists of overlapping the truncation and the integration boundaries of the standard method, so that the integral equation becomes singular as in the well-known Finite Element Method-Boundary Element Method (FEM-BEM) method. The new method is called FEM-SDBCI. Assuming an unknown Dirichlet condition on the truncation boundary, the global algebraic system is constituted by the sparse FEM equations and by the dense integral equations, in which singularities arise. Analytical formulas are provided to compute these singular integrals. The global system is solved by means of a Generalized Minimal Residual iterative procedure. Findings – The proposed method leads to slightly less accurate numerical results than FEM-BEM, but the latter requires much more computing time. Practical implications – Then FEM-SDBCI appears more appropriate than FEM-BEM for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Originality/value – Note that FEM-SDBCI assumes a Dirichlet condition on the truncation boundary, whereas FEM-BEM assumes a Neumann one.

scholarly journals Locally and Remotely Forced Subtropical AMOC Variability: A Matter of Time Scales

2020 ◽  
Vol 33 (12) ◽  
pp. 5155-5172
Author(s):  
Quentin Jamet ◽  
William K. Dewar ◽  
Nicolas Wienders ◽  
Bruno Deremble ◽  
Sally Close ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
North Atlantic ◽  
Time Scale ◽  
Low Frequency ◽  
Meridional Overturning Circulation ◽  
Open Boundary ◽  
Overturning Circulation ◽  
Decadal Scale ◽  
Meridional Overturning

AbstractMechanisms driving the North Atlantic meridional overturning circulation (AMOC) variability at low frequency are of central interest for accurate climate predictions. Although the subpolar gyre region has been identified as a preferred place for generating climate time-scale signals, their southward propagation remains under consideration, complicating the interpretation of the observed time series provided by the Rapid Climate Change–Meridional Overturning Circulation and Heatflux Array–Western Boundary Time Series (RAPID–MOCHA–WBTS) program. In this study, we aim at disentangling the respective contribution of the local atmospheric forcing from signals of remote origin for the subtropical low-frequency AMOC variability. We analyze for this a set of four ensembles of a regional (20°S–55°N), eddy-resolving (1/12°) North Atlantic oceanic configuration, where surface forcing and open boundary conditions are alternatively permuted from fully varying (realistic) to yearly repeating signals. Their analysis reveals the predominance of local, atmospherically forced signal at interannual time scales (2–10 years), whereas signals imposed by the boundaries are responsible for the decadal (10–30 years) part of the spectrum. Due to this marked time-scale separation, we show that, although the intergyre region exhibits peculiarities, most of the subtropical AMOC variability can be understood as a linear superposition of these two signals. Finally, we find that the decadal-scale, boundary-forced AMOC variability has both northern and southern origins, although the former dominates over the latter, including at the site of the RAPID array (26.5°N).

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