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Consistent modeling of boundaries in acoustic finite-difference time-domain simulations
KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
University of Texas.
2012 (Engelska)Ingår i: Journal of the Acoustical Society of America, ISSN 0001-4966, E-ISSN 1520-8524, Vol. 132, nr 3, s. 1303-1310Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

The finite-difference time-domain method is one of the most popular for wave propagation in the time domain. One of its advantages is the use of a structured staggered grid, which makes it simple and efficient on modern computer architectures. A drawback however is the difficulty in approximating oblique boundaries, having to resort to staircase approximations.  In many scattering problems this means that the grid resolution required to obtain an accurate solution is much higher than what is dictated by propagation in a homogeneous material.  In this paper zero boundary data is considered, first for the velocity and then the pressure. These two forms of boundary conditions model perfectly rigid and pressure-release boundaries, respectively.  A simple and efficient method to consistently model curved rigid boundaries in two dimensions was developed in [A.-K. Tornberg and B. Engquist, J. Comput. Phys. 227, 6922--6943 (2008)].  Here this treatment is generalized to three dimensions.  Based on the approach of this method, a technique to model pressure-release surfaces with second order accuracy and without additional restriction on the timestep is also introduced.  The structure of the standard method is preserved, making it easy to use in existing solvers.  The effectiveness is demonstrated in several numerical tests.

Ort, förlag, år, upplaga, sidor
Acoustical Society of America (ASA), 2012. Vol. 132, nr 3, s. 1303-1310
Nyckelord [en]
Computer architecture, Finite difference time domain method
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
URN: urn:nbn:se:kth:diva-63593DOI: 10.1121/1.4740490ISI: 000309155000021Scopus ID: 2-s2.0-84866306609OAI: oai:DiVA.org:kth-63593DiVA, id: diva2:482429
Forskningsfinansiär
Swedish e‐Science Research Center
Anmärkning

QC 20121031

Tillgänglig från: 2012-01-23 Skapad: 2012-01-23 Senast uppdaterad: 2017-12-08Bibliografiskt granskad
Ingår i avhandling
1. Modified Stencils for Boundaries and Subgrid Scales in the Finite-Difference Time-Domain Method
Öppna denna publikation i ny flik eller fönster >>Modified Stencils for Boundaries and Subgrid Scales in the Finite-Difference Time-Domain Method
2012 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
Abstract [en]

This thesis centers on modified stencils for the Finite-Difference Time-Domain method (FDTD), or Yee scheme, when modelling curved boundaries, obstacles and holes smaller than the discretization length.  The goal is to increase the accuracy while keeping the structure of the standard method, enabling improvements to existing implementations with minimal effort.

We present an extension of a previously developed technique for consistent boundary approximation in the Yee scheme.  We consider both Maxwell's equations and the acoustic equations in three dimensions, which require separate treatment, unlike in two dimensions.

The stability properties of coefficient modifications are essential for practical usability.  We present an analysis of the requirements for time-stable modifications, which we use to construct a simple and effective method for boundary approximations. The method starts from a predetermined staircase discretization of the boundary, requiring no further data on the underlying geometry that is being approximated.

Not only is the standard staircasing of curved boundaries a poor approximation, it is inconsistent, giving rise to errors that do not disappear in the limit of small grid lengths. We analyze the standard staircase approximation by deriving exact solutions of the difference equations, including the staircase boundary. This facilitates a detailed error analysis, showing how staircasing affects amplitude, phase, frequency and attenuation of waves.

To model obstacles and holes of smaller size than the grid length, we develop a numerical subgrid method based on locally modified stencils, where a highly resolved micro problem is used to generate effective coefficients for the Yee scheme at the macro scale.

The implementations and analysis of the developed methods are validated through systematic numerical tests.

Ort, förlag, år, upplaga, sidor
Stockholm: KTH Royal Institute of Technology, 2012. s. xi, 34
Serie
Trita-CSC-A, ISSN 1653-5723 ; 2012:07
Nyckelord
FDTD, Yee, Staircasing
Nationell ämneskategori
Beräkningsmatematik
Identifikatorer
urn:nbn:se:kth:diva-95510 (URN)978-91-7501-417-3 (ISBN)
Disputation
2012-06-15, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (Engelska)
Opponent
Handledare
Forskningsfinansiär
Swedish e‐Science Research Center
Anmärkning

QC 20120530

Tillgänglig från: 2012-05-30 Skapad: 2012-05-28 Senast uppdaterad: 2013-04-09Bibliografiskt granskad

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Häggblad, JonEngquist, Björn
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Numerisk analys, NA (stängd 2012-06-30)
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Journal of the Acoustical Society of America
Beräkningsmatematik

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