Rohit R. Deokar
University of Minnesota
ParticleGeometric modelingLow frequencyDegrees of freedom (mechanics)AlgorithmSpace (mathematics)Current (mathematics)Basis (linear algebra)Newmark-beta methodRandomnessMathematical optimizationTopologyRadiologyEngineeringWork (thermodynamics)Finite element methodDimension (vector space)SurgeryNonlinear systemComputational fluid dynamicsModeling and simulationThermal conductionLeast squaresPerturbation (astronomy)Universality (dynamical systems)EstimatorDifferential algebraic equationEnergy (signal processing)Galerkin methodMaterials scienceMonte Carlo methodMedical physicsSpeed of soundCompliance (physiology)AtherectomyPetrov–Galerkin methodScale (ratio)Optical coherence tomographyModel order reductionAngioplastyFlexibility (engineering)Isogeometric analysisOrder (ring theory)Applied mathematicsExplicit time integrationProper orthogonal decompositionMulti dimensionalEngineering simulationFull orderReduced orderOrbital atherectomyTissue damageTransient (oscillation)MathematicsComputer scienceComputer simulationIncompressible flowHeat transferOrdinary differential equationVariational integratorRate of convergenceMechanicsControl theoryLinear multistep methodDegrees of freedom (statistics)Convergence (routing)MedicineDiscretizationA priori and a posterioriDynamical systems theoryIntegratorStochastic processMidpoint methodSpace timeDynamic problemDissipative system
13Publications
7H-index
70Citations
Publications 13
Newest
#1Chensen Ding (Hunan University)H-Index: 8
#2Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
Last. Stéphane Bordas (Cardiff University)H-Index: 67
view all 8 authors...
Abstract After space discretization employing traditional dynamic isogeometric analysis of structures (composite type) with/without dissimilar materials, the issues that persist include either using numerically non-dissipative time integration algorithms that induces the high frequency participation (oscillations) in solution, or using dissipative algorithms that can dampen the high frequency participation but simultaneously induce significant loss of total energy of the system. To circumvent th...
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#1Chensen Ding (Hunan University)H-Index: 8
#2Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
Last. Stéphane Bordas (Cardiff University)H-Index: 67
view all 7 authors...
Abstract Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially uncorrelated material uncertainties. They are not representative of realistic and practical engineering situations. In particular, it is more serious for composite structures comprised of dissimilar materials. Therefore, we propose a novel model order reduction via proper orthogonal decom...
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#1Dean Maxam (UMN: University of Minnesota)H-Index: 3
#2Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 3 authors...
AbstractA robust proper orthogonal decomposition technique is applied to develop reduced-order models (ROMs) for time-dependent thermal stress problems that are arbitrarily discretized with multiple sub-domains to provide flexibility and generality in the sense that different spatial methods and different time integration algorithms can be employed in a single analysis. This approach enables large computational savings for model problems with either/both transient thermal and dynamic structural ...
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#1Chensen Ding (Hunan University)H-Index: 8
#2Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 6 authors...
This paper develops a proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties. The geometry of the structure is exactly represented and more accurate deterministic solutions are provided via isogeometric analysis (IGA). Secondly, we innovatively tackle multi-dimensional uncertainties, including separate material, geometric and force randomness, and their combined cases. Thirdly, MCS is employed to solve the m...
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#1Dean Maxam (UMN: University of Minnesota)H-Index: 3
#2Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 3 authors...
AbstractA novel and general computational methodology for thermal stress problems with multiple subdomains is presented under the unified generalized single-step single-solve (GSSSS) framework for first- and second-order differential algebraic equations. It enables arbitrary number of subdomains and the coupling of different but compatible time-stepping algorithms ensuring second-order time accuracy in all differential and algebraic variables. The framework permits implicit/explicit coupling and...
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#1Chensen Ding (Hunan University)H-Index: 8
#2Xiangyang Cui (Hunan University)H-Index: 36
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 6 authors...
AbstractThe contribution herein proposes a novel generalized nth order perturbation isogeometric method (GNP-IGA) for efficient steady heat transfer stochastic analysis with material uncertainty. W...
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#1Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
#2Dean Maxam (UMN: University of Minnesota)H-Index: 3
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 3 authors...
Abstract A novel general purpose a posteriori error estimator that is agnostic to selection of time integration schemes arising under the umbrella of ”Generalized Single Step Single Solve” (GSSSS) framework and family of algorithms is proposed to foster adaptive time stepping; it encompasses the entire class of LMS methods for second order dynamical systems. Unlike several error estimators that have been applied to a limited selection of known time integration methods found in the literature, th...
Source
#1Chensen Ding (Hunan University)H-Index: 8
#2Xiangyang Cui (Hunan University)H-Index: 36
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 6 authors...
AbstractThis article develops an isogeometric independent coefficients (IGA-IC) reduced order method for transient nonlinear heat conduction analysis. Herein, we first exactly represent the geometr...
Source
#1Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
#2Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
Abstract A novel model order reduction framework for space and time domain discretizations is proposed. Iterative convergence of a Galerkin approximation in space and a Least Squares Petrov Galerkin approximation in time is obtained through a staggered reduced basis method in space-time. In every iteration, one of the two domains (space or time) is refined; and the other is reduced and a posteriori error indicators in space and time are used to drive the convergence iterations. Numerical results...
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#1Rohit R. Deokar (UMN: University of Minnesota)H-Index: 7
#2Masao Shimada (UMN: University of Minnesota)H-Index: 6
Last. Kumar K. Tamma (UMN: University of Minnesota)H-Index: 30
view all 4 authors...
Abstract A new numerical strategy to remedy high-frequency issues caused by finite element discretization in structural dynamic problems has been proposed. A noteworthy characteristic of this advocated approach is that it is based upon the use of the proper orthogonal decomposition (POD) incorporated in conjunction with implicit or explicit numerically non-dissipative time integration schemes to substantially improve or eliminate undesirable effects due to high-frequency instabilities. Original ...
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