A coupled IGA–Meshfree discretization of arbitrary order of accuracy and without global geometry parameterization

Valizadeh, Navid; Bazilevs, Yuri; Chen, J. S.; Rabczuk, Timon

doi:10.1016/j.cma.2015.04.002

Cited by 56 publications

(17 citation statements)

References 39 publications

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“…This approach uses pixel data obtained from medical images which are used as nodes for domain discretization in the meshless modeling. Valizadeh et al [32] implemented a 3D patient specific leg-muscle pixel-based model using isogeometric analysis (IGA) and the RKPM.…”

Section: Skeletal Muscle Simulationsmentioning

confidence: 99%

Simulation of Skeletal Muscles in Real-Time with Parallel Computing in GPU

Navarro-Hinojosa

Alencastre-Miranda

2020

Applied Sciences

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Modeling and simulation of the skeletal muscles are usually solved using the Finite Element method (FEM) which, although accurate, commonly needs a complex mesh and the solution is not processed in real-time. In this work, a meshfree model that simulates skeletal muscles considering their functioning and control based on electrical activity, their structure based on biological tissue, and that computes in real-time, is presented. Meshfree methods were used because they are able to surpass most of the limitations that are present in mesh-based methods. The muscular belly was modelled as a particle-based viscoelastic fluid, which is controlled using the monodomain model and shape matching. The smoothed particle hydrodynamics (SPH) method was used to solve both the fluid dynamics and the electrophysiological model. To analyze the accuracy of the method, a similar model was implemented with FEM. Both FEM and SPH methods provide similar solutions of the models in terms of pressure and displacement, with an error of around 0.09, with up to a 10% difference between them. Through the use of General-purpose computing on graphics processing units (GPGPU), real-time simulations that offer a viable alternative to mesh-based models for interactive biological tissue simulations was achieved.

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Section: Skeletal Muscle Simulationsmentioning

confidence: 99%

Simulation of Skeletal Muscles in Real-Time with Parallel Computing in GPU

Navarro-Hinojosa

Alencastre-Miranda

2020

Applied Sciences

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“…As the tensor product mesh has been a limitation in conventional isogeometric analysis, combinations of various meshfree methods and IGA have been developed by many researchers and applied successfully in many fields [17][18][19][20]. In meshfree methods, the domain of a problem is represented, ideally, only by a set of arbitrarily distributed nodes.…”

Section: Introductionmentioning

confidence: 99%

“…It follows from the Kronecker δ function property of the RPIM that boundary constraints can be directly applied to the field nodes. Then, Equation (16) can be rewritten as KU = F (17) which is the final discretization equation shaped by the meshfree RPIM. When the linear equation in Equation (17) is solved, the displacement U of all field nodes will be gained, and the stress σ can be recovered from:…”

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confidence: 99%

NURBS-Enhanced Meshfree Method with an Integration Subtraction Technique for Complex Topology

et al. 2020

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In this paper, we present an integration subtraction technique to model holes interactively in a predesigned domain for adaptive problems. This technique involves two approaches, the normal subtraction technique and the moving subtraction technique. In the basic normal subtraction technique, the predesigned domain can be meshed using any methods as an initial integration background cell for meshfree analysis. Holes are described using closed non-uniform rational B-spline (NURBS) curves to preserve the exact computer-aided design (CAD) geometry and are meshed alone using the homotopic method, so they can easily be subtracted from the predesigned domain with no refinement. On the other hand, when the hole size is varying, the moving subtraction technique, in which only the changing part between the new and old boundaries needs to be integrated and subtracted, is more efficient. Compared with the standard radial point interpolation method (RPIM) and finite element method (FEM) in three linear elastic examples with different holes, the excellent accuracy and good efficiency of the proposed method are demonstrated, and its feasibility in complex topology problems is verified.

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“…The volume discretization can be challenging for the IGA method, whereas it can be readily solved by meshfree methods. Valizadeh et al combined the IGA method with the RKPM method in the physical domain to avoid global geometry parameterization. In this way, the basis functions are constructed directly in the physical domain without requiring global geometry parameterization in RKPM.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric‐meshfree coupling approach for analysis of cracks

Nguyen‐Thanh

Huang

Zhou

2017

Numerical Meth Engineering

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Summary This paper presents a new concurrent simulation approach to couple isogeometric analysis (IGA) with the meshfree method for studying of crack problems. In the present method, the overall physical domain is divided into 2 subdomains that are formulated with the IGA and meshfree method, respectively. In the meshfree subdomain, the moving least squares shape function is adopted for the discretization of the area around crack tips, and the IGA subdomain is adopted in the remaining area. Meanwhile, the interface region between the 2 subdomains is represented by coupled shape functions. The resulting shape function, which comprises both IGA and meshfree shape functions, satisfies the consistency condition, thus ensuring convergence of the method. Moreover, the meshfree shape functions augmented with the enriched basis functions to predict the singular stress fields near a crack tip are presented. The proposed approach is also applied to simulate the crack propagation under a mixed‐mode condition. Several numerical examples are studied to demonstrate the use and robustness of the proposed method.

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A coupled IGA–Meshfree discretization of arbitrary order of accuracy and without global geometry parameterization

Cited by 56 publications

References 39 publications

Simulation of Skeletal Muscles in Real-Time with Parallel Computing in GPU

Simulation of Skeletal Muscles in Real-Time with Parallel Computing in GPU

NURBS-Enhanced Meshfree Method with an Integration Subtraction Technique for Complex Topology

An isogeometric‐meshfree coupling approach for analysis of cracks

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