Numerical integration of partial differential equations using principles of multidimensional wave digital filters

Fettweis, A.; Nitsche, Gunnar

doi:10.1007/bf00927832

Cited by 93 publications

(63 citation statements)

References 11 publications

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“…Applying the standard procedure known from the MD wave digital filtering [4,5] for transforming the set of PDEs to its equivalent discrete passive model, a lumped MD-passive Kirchhoff circuit (MDKC) and its discrete approximation of MDWDF network [11] depicted in Figures 1(a) and 1(b), respectively, are obtained for the numerical integration of the LSW system. Since the resulting network behaves in the same way as the continuous one, it also preserves passivity for the discrete dynamical system, thus ensuring full robustness and stability of the algorithm [4,12].…”

Section: Lsw System and Its Corresponding Multidimensionalmentioning

confidence: 99%

“…Built on properties of the traveling wave formulation of lumped electrical elements to the modeling and simulation of a system represented by PDEs, a novel approach named wave digital filtering (WDF) network [3] had been proposed in the past due to its excellent features that fit requirements of practical interest [4,5]. Unlike most types of digital filter, every delay element in a WDF network can be interpreted physically as holding the current state of a mass or spring (or capacitor or inductors) [3].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Parallel Multidimensional Wave Digital Filtering Network on IBM Cell Broadband Engine

Tseng

2014

Journal of Computational Engineering

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As an alternative approach for the numerical integration of physical systems, the MDWDF technique has become of importance in the field of numerical analysis due to its attractive features, for example, massive parallelism and high accuracy both inherent in nature. In this study, speed-up efficiencies of a MDWDF network are studied for the linearized shallow water system, which plays an important role in fluid dynamics. To achieve the goal, the full parallelism of the MDWDF network is established in the first place based on the chained MD retiming technique. Following the implementation on the IBM Cell Broadband Engine (Cell/BE), excellent performance of the full parallel architecture is revealed. The IBM Cell/BE containing 1 power processor element (PPE) and 8 synergistic processor elements (SPEs) perfectly fits the architecture of the retimed MDWDF model. Empirical results have demonstrated that the full parallelized model with 8 processors (1PPE + 7SPEs) outperforms the other three models: partial right/left-loop retimed models and the full sequential model with 4× improvements for scheduled grids 51 × 51. In addition, for scheduled fine grids 201 × 201, the full parallel model is shown to possess significant performance over these models by up to 7× improvements.

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Section: Lsw System and Its Corresponding Multidimensionalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of Parallel Multidimensional Wave Digital Filtering Network on IBM Cell Broadband Engine

Tseng

2014

Journal of Computational Engineering

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“…A unifying treatment of the theory and application of wave digital filters is given in the classical paper (Fettweis, 1986). Later this principle was extended to distributed parameter systems, described by partial differential equations (Fettweis and Nitsche, 1991). Modern descriptions of the wave digital principle as a tool for numerical integration and modeling are given in (Ochs, 2001;Bilbao, 2004;Välimäki et al, 2006;Smith, 2007).…”

Section: Wave Digital Principlementioning

confidence: 99%

“…Applications to distributed parameter systems were discussed, e.g., in (Fettweis and Nitsche, 1991;Fettweis, 1992;Rabenstein and Trautmann, 2003) The theory of the wave digital principle is well founded on the theory of analog electrical networks, signals and systems, and digital signal processing. After many refinements and extensions (even to the theory of relativity (Fettweis, 2002)), it can be considered a rather mature field.…”

Section: Summary Of the One-dimensional Wave Digital Approachmentioning

confidence: 99%

Block-Based Physical Modeling with Applications in Musical Acoustics

Rabenstein¹,

Petrausch²

2008

International Journal of Applied Mathematics and Computer Science

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Block-based physical modeling is a methodology for modeling physical systems with different subsystems. Each subsystem may be modeled according to a different paradigm. Connecting systems of diverse nature in the discrete-time domain requires a unified interconnection strategy. Such a strategy is provided by the well-known wave digital principle, which had been introduced initially for the design of digital filters. It serves as a starting point for the more general idea of blockbased physical modeling, where arbitrary discrete-time state space representations can communicate via wave variables. An example in musical acoustics shows the application of block-based modeling to multidimensional physical systems.

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“…This concept has also successfully been applied to numerical solutions of ordinary differential equations by digital simulation of nonlinear circuits, even with chaotic behavior [5][6][7][8]. Parallel to this development, the concept has been extended to multidimensional wave digital filters in order to numerically integrate partial differential equations [9][10][11]. But it would be too superficial to regard the wave digital concept merely as a simulation tool.…”

Section: Introductionmentioning

confidence: 99%

Wave digital simulation of passive systems in linear state‐space form

Ochs

2009

Int J Numerical Modelling

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SUMMARYThis paper deals with wave digital modeling of passive state-space models. The set of differential equations must be of linear state-space form, but all parameters can be time-variant and/or nonlinear. For such statespace models, a canonical internally passive reference circuit is presented and used for deriving wave digital structures. In order to show the usability, special solutions for important basic linear time-variant models are compared with wave digital simulation results. Moreover, the wave digital modeling of a nonlinear and time-variant oscillator is discussed. Especially for a lossless oscillator an implementation is proposed, which preserves energy under finite-arithmetic conditions. This is verified by comparing simulation results with the analytical solution of a gravity pendulum.

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Numerical integration of partial differential equations using principles of multidimensional wave digital filters

Cited by 93 publications

References 11 publications

Analysis of Parallel Multidimensional Wave Digital Filtering Network on IBM Cell Broadband Engine

Analysis of Parallel Multidimensional Wave Digital Filtering Network on IBM Cell Broadband Engine

Block-Based Physical Modeling with Applications in Musical Acoustics

Wave digital simulation of passive systems in linear state‐space form

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