Hybrid perfectly-matched-layers for transient simulation of scalar elastic waves

Pakravan, Alireza,Kang, Jun Won,Newtson, Craig M.,Kallivokas, Loukas F. Techno-Press 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.4

This paper presents a new formulation for forward scalar wave simulations in semi-infinite media. Perfectly-Matched-Layers (PMLs) are used as a wave absorbing boundary layer to surround a finite computational domain truncated from the semi-infinite domain. In this work, a hybrid formulation was developed for the simulation of scalar wave motion in two-dimensional PML-truncated domains. In this formulation, displacements and stresses are considered as unknowns in the PML domain, while only displacements are considered to be unknowns in the interior domain. This formulation reduces computational cost compared to fully-mixed formulations. To obtain governing wave equations in the PML region, complex coordinate stretching transformation was introduced to equilibrium, constitutive, and compatibility equations in the frequency domain. Then, equations were converted back to the time-domain using the inverse Fourier transform. The resulting equations are mixed (contain both displacements and stresses), and are coupled with the displacement-only equation in the regular domain. The Newmark method was used for the time integration of the semi-discrete equations.

A Gauss–Newton full-waveform inversion in PML-truncated domains using scalar probing waves

Pakravan, Alireza,Kang, Jun Won,Newtson, Craig M. Elsevier 2017 Journal of computational physics Vol.350 No.-

<P><B>Abstract</B></P> <P>This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss–Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush–Kuhn–Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss–Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A Gauss–Newton full-waveform inversion approach combined with a hybrid unsplit-field PML has been developed. </LI> <LI> The proposed inversion method improves the accuracy and efficiency of solutions compared to existing inversion methods. </LI> <LI> The proposed full-waveform inversion algorithm is robust even in the presence of noise in measured responses. </LI> </UL> </P>

하이브리드 Perfectly-Matched-Layers를 이용한 탄성매질에서의 SH-파동 전파 해석

Pakravan, Alireza,강준원(Kang, Jun Won) 대한토목학회 2013 대한토목학회 학술대회 Vol.2013 No.10

Hybrid perfectly-matched-layers for transient simulation of scalar elastic waves

Alireza Pakravan,강준원,Craig M. Newtson,Loukas F. Kallivokas 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.51 No.4

This paper presents a new formulation for forward scalar wave simulations in semi-infinite media. Perfectly-Matched-Layers (PMLs) are used as a wave absorbing boundary layer to surround a finite computational domain truncated from the semi-infinite domain. In this work, a hybrid formulation was developed for the simulation of scalar wave motion in two-dimensional PML-truncated domains. In this formulation, displacements and stresses are considered as unknowns in the PML domain, while only displacements are considered to be unknowns in the interior domain. This formulation reduces computational cost compared to fully-mixed formulations. To obtain governing wave equations in the PML region, complex coordinate stretching transformation was introduced to equilibrium, constitutive, andcompatibility equations in the frequency domain. Then, equations were converted back to the time-domain using the inverse Fourier transform. The resulting equations are mixed (contain both displacements and stresses), and are coupled with the displacement-only equation in the regular domain. The Newmark methodwas used for the time integration of the semi-discrete equations.

A Gauss-Newton Full-waveform Inversion for Material Profile Reconstruction in 1D PML-truncated Solid Media

Alireza Pakravan,강준원 대한토목학회 2014 KSCE JOURNAL OF CIVIL ENGINEERING Vol.18 No.6

This paper discusses a Gauss-Newton full-waveform inversion procedure for material profile reconstruction in semi-infinite solidmedia. Given surficial measurements of the solid’s response to interrogating waves, the procedure seeks to find an unknown wavevelocity profile within a computational domain truncated by Perfectly-Matched-Layer (PML) wave-absorbing boundaries. To thisend, the inversion procedure minimizes a Lagrangian functional composed of a cost functional augmented by PML-endowed waveequations via Lagrange multipliers. Enforcing the stationarity of the Lagrangian leads to KKT (Karush-Kuhn-Tucker) conditionscomprising time-dependent state, adjoint, and time-invariant control problems. The material parameter is updated by iterativelysolving the KKT conditions in the reduced space of the control variable. The update of the control variable is determined by a Gauss-Newton-Krylov optimization algorithms. Super-linear convergence behavior of the Gauss-Newton inversion has been observed inone-dimensional implementations. Regularization and frequency-continuation schemes were used to relieve the ill-posedness of theinverse problem.

Relationship between the surface free energy of hardened cement paste and chemical phase composition

H.R. Pakravan,M. Jamshidi,M. Latifi 한국공업화학회 2014 Journal of Industrial and Engineering Chemistry Vol.20 No.4

Special emphasis is put on to correlating the changes in phase composition with wettability of hardened cement paste. The results were found in contradiction, because it was demonstrated by XRD analysis that by increment in curing ages, high energy products are developed in the matrix which increases surface free energy. In contrast, surface evaporation of the water and bulk hydration cause a decrease in hydrophilic properties of the surface free energy. It was concluded that the latter phenomenon has more important impact than surface free energy. Crown Copyright

시간영역 Gauss-Newton 전체파형 역해석 기법의 성능평가

강준원,Kang, Jun Won,Pakravan, Alireza 한국전산구조공학회 2013 한국전산구조공학회논문집 Vol.26 No.4

본 논문에서는 물성이 균일하지 않은 반무한 고체영역의 탄성파속도 분포를 재구성하기 위한 시간영역 Gauss-Newton 전체파형 역해석 기법을 소개한다. 반무한 영역을 유한 계산영역으로 치환하기 위하여 유한영역의 경계에 수치적 파동흡수 경계조건인 perfectly-matched-layers(PMLs)를 도입하였다. 이 역해석 문제는 PML을 경계로 하는 영역에서의 탄성파동방정식을 구속조건으로 하는 최적화 문제로 성립되며, 표면에서 측정된 변위응답과 혼합유한요소법에 의해 계산된 응답간의 차이를 최소화함으로써 미지의 탄성파속도 분포를 결정한다. 이 과정에서 Gauss-Newton-Krylov 최적화 알고리즘과 정규화기법을 사용하여 탄성파속도의 분포를 반복적으로 업데이트하였다. 1차원 수치예제들을 통해 Gauss-Newton 역해석으로 부터 재구성된 탄성파속도의 분포가 목표값에 충분히 근사함을 보였으며, Fletcher Reeves 최적화 알고리즘을 사용한 기존의 역해석 결과에 비해 수렴율이 현저히 개선되고 계산 소요시간이 단축됨을 확인할 수 있었다. This paper presents a time-domain Gauss-Newton full-waveform inversion method for the material profile reconstruction in heterogeneous semi-infinite solid media. To implement the inverse problem in a finite computational domain, perfectly-matchedlayers( PMLs) are introduced as wave-absorbing boundaries within which the domain's wave velocity profile is to be reconstructed. The inverse problem is formulated in a partial-differential-equations(PDE)-constrained optimization framework, where a least-squares misfit between measured and calculated surface responses is minimized under the constraint of PML-endowed wave equations. A Gauss-Newton-Krylov optimization algorithm is utilized to iteratively update the unknown wave velocity profile with the aid of a specialized regularization scheme. Through a series of one-dimensional examples, the solution of the Gauss-Newton inversion was close enough to the target profile, and showed superior convergence behavior with reduced wall-clock time of implementation compared to a conventional inversion using Fletcher-Reeves optimization algorithm.

Improvement and Comparative Study of Control Theory-based AQMMethods for Networks with Realistic Traffic

N. Bigdeli,M. Haeri,M.R. Pakravan 제어로봇시스템학회 2004 제어로봇시스템학회 국제학술대회 논문집 Vol.2004 No.8