Research in Scientific Computation - SERC

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Background ● ● ● Spatially Discretized Structures (PDEs) via the Finite Element or Boundary Element Method yield stiff finite dimensional systems that have small amplitude high frequency responses. Spatial Discretizations tend to more erroneously estimate the higher frequencies (Babuska). Hence it is computationally profitable to damp out small amplitude responses in the corresponding modes. Deterministic models have traditionally used the Newmark Beta Method, HHTalpha method, WBZalpha method, HoffPahl method to do this.
Generalizedalpha Method (Chung and Hulbert) ● ● ● Generalization of the numerically dissipative schemes for deterministic equations of structural dynamics. User selectable parameter ∈ [0,1] for calibrating numerical dissipation to the response. AStable for all practical purposes. (spectral radius of the amplification matrix is meromorphic with two poles on C.) The spectral radius of the amplification matrix is 1 for low frequencies (near the origin on the imaginary axis) for all values of . As the absolute value of the imaginary part on the stability plane increases, it tends to be .
Page 1 and 2: Research in Scientific Computation
Page 3 and 4: Constrained Dynamics Models in ●
Page 5 and 6: Cell Dynamics ● ● ● Multiscal
Page 7 and 8: Classical Dynamics Approach 2 d X M
Page 9: Micromechanical System: CMOS fabr
Page 13 and 14: ● Second Order SDE Structural dyn
Page 15 and 16: ItoTaylor Expansion Strong order
Page 17 and 18: The Stochastic alpha Method x n1 =x
Page 19 and 20: Spectral Radius of the Amplificatio
Page 21 and 22: Stochastic Perturbation ● ● We
Page 23 and 24: Parameters and ≈ 1− 2 h 16 O
Page 25 and 26: Stability: Schur Decomposition of A
Page 27 and 28: ● Asymptotic Stability As ∣∣0
Page 29 and 30: Elastic Beam ● Elastic beam clamp
Page 31 and 32: dx=u dt dy =v dt d =w dt Noisy Bush
Page 34 and 35: Further Research Opportunities ●
Page 36 and 37: Optimal Control Problem 1 Minimize
Page 38 and 39: Control of a Linear Train x_i x_n x
Page 40 and 41: ● ● ● ● ● Issues with Hig
Page 42 and 43: Simplified Overview of SQP ● ●
Page 44 and 45: Basis Matrix and High Index ● ●
Page 46 and 47: ● ● ● Perturbing Discretizati
Page 48 and 49: Perturbation theory of Singular Val
Page 50 and 51: Generalized Alpha Method (contd)
Page 52 and 53: Structure of the (DAE) Basis Matrix
Page 54 and 55: Equivalence of Transcription Formul
Page 57 and 58: Reentry of a Reusable Launch Vehicl
Page 59 and 60: ● ● Converges for rho = 0.75 do
Page 61:
Further Research ● ● ● Onli
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Research in Scientific Computation - SERC

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