Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework
In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phasefield models, by taking advantage of the high-continuity of the basis functions granted by the isogeometri...
| Main Authors: | Côrtes, A., Vignal, P., Sarmiento, A., García, D., Collier, N., Dalcin, L., Calo, Victor |
|---|---|
| Format: | Conference Paper |
| Published: |
2014
|
| Online Access: | http://hdl.handle.net/20.500.11937/51582 |
Similar Items
PetIGA: A framework for high-performance isogeometric analysis
by: Dalcin, L., et al.
Published: (2016)
by: Dalcin, L., et al.
Published: (2016)
Modeling phase-transitions using a high-performance, isogeometric analysis framework
by: Vignal, P., et al.
Published: (2014)
by: Vignal, P., et al.
Published: (2014)
Coupling Navier-Stokes and Cahn-Hilliard equations in a two-dimensional annular flow configuration
by: Vignal, P., et al.
Published: (2015)
by: Vignal, P., et al.
Published: (2015)
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
by: Collier, N., et al.
Published: (2014)
by: Collier, N., et al.
Published: (2014)
PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces
by: Sarmiento, A., et al.
Published: (2017)
by: Sarmiento, A., et al.
Published: (2017)
The cost of continuity: Performance of iterative solvers on isogeometric finite elements
by: Collier, N., et al.
Published: (2013)
by: Collier, N., et al.
Published: (2013)
The value of continuity: Refined isogeometric analysis and fast direct solvers
by: Garcia, D., et al.
Published: (2016)
by: Garcia, D., et al.
Published: (2016)
Isogeometric shell formulation based on a classical shell model
by: Niemi, A., et al.
Published: (2012)
by: Niemi, A., et al.
Published: (2012)
Refined Isogeometric Analysis for a preconditioned conjugate gradient solver
by: Garcia, D., et al.
Published: (2018)
by: Garcia, D., et al.
Published: (2018)
Optimal spectral approximation of 2n-order differential operators by mixed isogeometric analysis
by: Deng, Quanling, et al.
Published: (2019)
by: Deng, Quanling, et al.
Published: (2019)
Isogeometric spectral approximation for elliptic differential operators
by: Deng, Quanling, et al.
Published: (2018)
by: Deng, Quanling, et al.
Published: (2018)
Convergence rates for diffusive shallow water equations (DSW) using higher order polynomials
by: Radwan, H., et al.
Published: (2012)
by: Radwan, H., et al.
Published: (2012)
The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers
by: Collier, N., et al.
Published: (2012)
by: Collier, N., et al.
Published: (2012)
Comparison of high-order accurate schemes for solving the nonlinear viscous burgers equation
by: M. Elfaghi, Abdulhafid, et al.
Published: (2009)
by: M. Elfaghi, Abdulhafid, et al.
Published: (2009)
Parallel Fast Isogeometric Solvers for Explicit Dynamics
by: Wozniak, M., et al.
Published: (2017)
by: Wozniak, M., et al.
Published: (2017)
A scalable block-preconditioning strategy for divergence-conforming B-spline discretizations of the Stokes problem
by: Côrtes, A., et al.
Published: (2016)
by: Côrtes, A., et al.
Published: (2016)
An energy-stable convex splitting for the phase-field crystal equation
by: Vignal, P., et al.
Published: (2015)
by: Vignal, P., et al.
Published: (2015)
Comparison of high-order accurate schemes for solving the nonlinear viscous burgers equation
by: Elfaghi, Abdulhafid M., et al.
Published: (2009)
by: Elfaghi, Abdulhafid M., et al.
Published: (2009)
An energy-stable generalized-α method for the Swift-Hohenberg equation
by: Sarmiento, A., et al.
Published: (2017)
by: Sarmiento, A., et al.
Published: (2017)
Dispersion-minimized mass for isogeometric analysis
by: Deng, Quanling, et al.
Published: (2018)
by: Deng, Quanling, et al.
Published: (2018)
Fast isogeometric solvers for explicit dynamics
by: Gao, L., et al.
Published: (2014)
by: Gao, L., et al.
Published: (2014)
Runge-kutta type methods for solving high-order ordinary differential equations
by: Ghawadri, Nizam Ghannam Fayez
Published: (2018)
by: Ghawadri, Nizam Ghannam Fayez
Published: (2018)
Quadrature blending for isogeometric analysis
by: Calo, Victor, et al.
Published: (2017)
by: Calo, Victor, et al.
Published: (2017)
Isogeometric analysis of hyperelastic materials using petiGA
by: Bernal, L., et al.
Published: (2013)
by: Bernal, L., et al.
Published: (2013)
Computational cost of isogeometric multi-frontal solvers on parallel distributed memory machines
by: Wozniak, M., et al.
Published: (2015)
by: Wozniak, M., et al.
Published: (2015)
Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
by: Kammuji, M., et al.
Published: (2016)
by: Kammuji, M., et al.
Published: (2016)
Micropolar nano fluids using B-spline divergence conforming spaces
by: Sarmiento, A., et al.
Published: (2014)
by: Sarmiento, A., et al.
Published: (2014)
Micropolar fluids using B-spline divergence conforming spaces
by: Sarmiento, A., et al.
Published: (2014)
by: Sarmiento, A., et al.
Published: (2014)
Convergence of variational iteration method for solving singular partial differential equations of fractional order
by: Elbeleze, Asma Ali, et al.
Published: (2014)
by: Elbeleze, Asma Ali, et al.
Published: (2014)
Direct numerical methods for solving a class of third-order partial differential equations
by: Mechee, M., et al.
Published: (2014)
by: Mechee, M., et al.
Published: (2014)
Direct numerical method for solving a class of fourth-order partial differential equation
by: Hussain, Kasim Abbas, et al.
Published: (2016)
by: Hussain, Kasim Abbas, et al.
Published: (2016)
Energy exchange analysis in droplet dynamics via the Navier-Stokes-Cahn-Hilliard model
by: Espath, L., et al.
Published: (2016)
by: Espath, L., et al.
Published: (2016)
Dealing with periodic boundary conditions for 1D, 2D and 3D isogeometric finite element method
by: Los, M., et al.
Published: (2015)
by: Los, M., et al.
Published: (2015)
A New Algorithm of Geometric Mean for Solving High-Order Fredholm Integro-differential Equations
by: Aruchunan, E., et al.
Published: (2016)
by: Aruchunan, E., et al.
Published: (2016)
Transformation methods in the study of nonlinear partial differential equations
by: Sophocleous, Christodoulos
Published: (1991)
by: Sophocleous, Christodoulos
Published: (1991)
Some parallel numerical methods in solving partial differential equations
by: Alias, Norma, et al.
Published: (2010)
by: Alias, Norma, et al.
Published: (2010)
Rational methods for solving first order ordinary differential equation
by: Fairuz, A'in Nazifa
Published: (2019)
by: Fairuz, A'in Nazifa
Published: (2019)
Fourth-Order Spline Methods For
Solving Nonlinear Schrödinger
Equation
by: Ahmad, Azhar
Published: (2021)
by: Ahmad, Azhar
Published: (2021)
Time adaptivity in the diffusive wave approximation to the shallow water equations
by: Collier, N., et al.
Published: (2013)
by: Collier, N., et al.
Published: (2013)
Diffusive wave approximation to the shallow water equations: Computational approach
by: Collier, N., et al.
Published: (2011)
by: Collier, N., et al.
Published: (2011)
Similar Items
-
PetIGA: A framework for high-performance isogeometric analysis
by: Dalcin, L., et al.
Published: (2016) -
Modeling phase-transitions using a high-performance, isogeometric analysis framework
by: Vignal, P., et al.
Published: (2014) -
Coupling Navier-Stokes and Cahn-Hilliard equations in a two-dimensional annular flow configuration
by: Vignal, P., et al.
Published: (2015) -
On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers
by: Collier, N., et al.
Published: (2014) -
PetIGA-MF: A multi-field high-performance toolbox for structure-preserving B-splines spaces
by: Sarmiento, A., et al.
Published: (2017)