Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

From COMSOL to NGSolve:a very personal voyage

Philipp W. Schroeder

Institute for Numerical and Applied MathematicsGeorg-August-University Göttingen, Germany

2nd NGSolve User Meeting 2018

Georg-August-University Göttingen, Germany

4–6 July 2018

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 1 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Outline

1 Background

2 Finite element method

3 Linear/nonlinear solvers

4 Time-stepping

5 Conclusion

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 1 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Some brief COMSOL backgroundCOMSOL Multiphysics

commercial finite element packagehas a GUI from which everything can be controlleddifferent packages (modules) available:

electromagneticsstructural mechanics & acousticsfluid flow & heat transferchemical engineering

but: basic package (no specific modules) has all core functionalitythere exists a MATLAB interface

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Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

How did I come to COMSOL?

Universityused in (some) FEM lectures at University of Göttingen

students can compute FE solutions with only knowledge of PDEeverything else (weak formulation etc.) can be ignored

Industryinternship and master’s thesis in automotive industry

optimise thickness of thermal insulation for pressure tanksuse phase change material to improve performance of adsorber

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Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Why do I use NGSolve now?

Christoph Lehrenfeldcame to Göttingen in September 2016convinced me to come to 1st NGSolve user meeting

I am using NGSolve ever since!

General factors which are essential for mePython interface!!!forum on ngsolve.org(Christoph, of course ;) )

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 4 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

What do I use NGSolve for?

Incompressible Computational Fluid Dynamicstime-dependent incompressible Navier–Stokes equationsexactly divergence-free methodspressure-robustnesstreatment of dominant convection via upwinding

Kelvin–Helmholtz instability Decaying homogeneous turbulence

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Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Geometry and meshing

1D / 2D / 3D domains supportedsegm / trigs / quad / tet / hex / prism / pyramidhybrid meshes possiblecurved boundaries possibleno hanging nodes allowed

GUI very convenient to use8 periodicity complicated4 complicated meshes: relatively easy8 manual meshes: only after export

h-adaptivity: works pretty well

Python: sometimes complicated4 periodicity more natural8 manual meshes: complicated

h-adaptivity: coarsening?

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 6 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

FE spaces

H1, L2, H(div), H(curl)

8 cannot add more spaces manually8 H1: k ⩽ 78 L2: k ⩽ 10 (2D); ⩽ 7 (3D)8 H(div): k ⩽ 3 (2D); ⩽ 2 (3D)8 H(curl): k ⩽ 3 (2D); ⩽ 2 (3D)8 no facet spaces, no hybrid methods

4 can add whatever you like4 arbitrary high-order

This flexibility was my main reason to switch to NGSolve!

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 7 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Weak form → discrete system

variational formulation works pretty much the same wayaccuracy of numerical integration can be chosen

8 only scalar-valued input possible4 simply add nonlinear expressions8 static condensation???

4 InnerProduct()4 Assemble() / Apply()

RAM in COMSOLpossible not very economical...

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 8 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Linear systems

pardiso, mumps available

4 pardiso and mumps are integrated4 automatically performs reiteration4 (F)GMRES, BiCGStab, CG4 (h/p) multigrid, algebraic multigrid4 all kinds of smoothers

4 sparsecholesky4 BDDC works great for me

Iterative solvers in COMSOLWork good for H1 methods. But: I was not able to obtain good resultsfor H(div)...

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 9 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Nonlinear systems

4 Newton solver integrated4 detects nonlinearity and acts

accordingly4 works very robustly

basically no personal experience

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 10 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Implicit and explicit methods

4 BDF: adaptive order, adaptivetime-step

4 generalised-α: adaptivetime-step

4 (explicit) Dormand-Prince:adaptive time-step

4 whatever you can imaginepossible solution of nonlinearsystems necessary

IMEX in COMSOLBDF variant: possible, but not efficient. Runge–Kutta variant: not clearif possible.

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Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Conclusion

convenience / usability flexibility / performance

4 easy to get started4 very ‘foolproof’8 (possibly) not optimal for

research8 performance not competitive

good and convenient if nothing‘fancy’ is desiredtransparent (for commercialtool)

4 huge reference manual

4 great for research4 fast

extensive knowledge of FEMnecessary

Philipp W. Schroeder (University of Göttingen) From COMSOL to NGSolve: a very personal voyage 12 / 12

Background Finite element method Linear/nonlinear solvers Time-stepping Conclusion

Thank you for your attention

Questions

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