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## Re: [Libmesh-users] error in newton iteration

 Re: [Libmesh-users] error in newton iteration From: Roy Stogner - 2005-12-21 18:38:03 ```On Wed, 21 Dec 2005, li pan wrote: > I used Newton iteration to solve a nonlinear elastic > problem. This method is embedded in a Newmark implicit > time integration. At the first several timestep the > Newton iteration convergenced very well (10 steps). Did you see quadratic convergence? The first thing you ought to check if Newton's method is behaving oddly is whether you get quadratic convergence as you approach the root - if not, then (assuming your linear solves are accurate enough) your Jacobian (i.e. your system matrix, not the geometric Jacobians) is probably inconsistent with your residual function. If that happens, your iteration can still converge, but the region of convergence may be smaller. Other possible problems: You may be starting from a bad initial guess. This has happened to me before, when I left junk in a solution vector. Depending on whether you're solving for the next timestep's solution or for the delta_solution, a relatively safe initial guess might be the previous timestep's solution or zero. The nonlinearities in your problem may be so bad that the region of covnergence is too small for you to hit with your initial guess. In that case you'll want to use a slower but safer method (successive approximation, perhaps, or continuation) to get close to the root followed by Newton to eliminate the last of your error. > The error could be numerical calculation of inversing matrix, > because I used simple Gauss elimination. I will apply the method of > Petsc. We've had some problems before with LASPACK not converging, but Gauss elimination isn't one of them - I often switch to complete LU factorization as a preconditioner when I'm trying to make sure that the linear solver isn't causing me problems. Gauss is bad because it's slow, not because it's inaccurate. --- Roy Stogner ```

 [Libmesh-users] error in newton iteration From: li pan - 2005-12-21 08:56:15 ```hi everyone, I used Newton iteration to solve a nonlinear elastic problem. This method is embedded in a Newmark implicit time integration. At the first several timestep the Newton iteration convergenced very well (10 steps). But afterwards it won't convergenced any more. It seems that the error which happened after each iteration was accumulated and became bigger and bigger. The error could be numerical calculation of inversing matrix, because I used simple Gauss elimination. I will apply the method of Petsc. Cound anybody tell me, is there any other reason which could cause such error. And how could I deal with it? best regards pan __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ```
 Re: [Libmesh-users] error in newton iteration From: Roy Stogner - 2005-12-21 18:38:03 ```On Wed, 21 Dec 2005, li pan wrote: > I used Newton iteration to solve a nonlinear elastic > problem. This method is embedded in a Newmark implicit > time integration. At the first several timestep the > Newton iteration convergenced very well (10 steps). Did you see quadratic convergence? The first thing you ought to check if Newton's method is behaving oddly is whether you get quadratic convergence as you approach the root - if not, then (assuming your linear solves are accurate enough) your Jacobian (i.e. your system matrix, not the geometric Jacobians) is probably inconsistent with your residual function. If that happens, your iteration can still converge, but the region of convergence may be smaller. Other possible problems: You may be starting from a bad initial guess. This has happened to me before, when I left junk in a solution vector. Depending on whether you're solving for the next timestep's solution or for the delta_solution, a relatively safe initial guess might be the previous timestep's solution or zero. The nonlinearities in your problem may be so bad that the region of covnergence is too small for you to hit with your initial guess. In that case you'll want to use a slower but safer method (successive approximation, perhaps, or continuation) to get close to the root followed by Newton to eliminate the last of your error. > The error could be numerical calculation of inversing matrix, > because I used simple Gauss elimination. I will apply the method of > Petsc. We've had some problems before with LASPACK not converging, but Gauss elimination isn't one of them - I often switch to complete LU factorization as a preconditioner when I'm trying to make sure that the linear solver isn't causing me problems. Gauss is bad because it's slow, not because it's inaccurate. --- Roy Stogner ```
 Re: [Libmesh-users] error in newton iteration From: Nachiket Gokhale - 2005-12-21 18:52:25 ```On Wed, 2005-12-21 at 12:38 -0600, Roy Stogner wrote: > On Wed, 21 Dec 2005, li pan wrote: > > > I used Newton iteration to solve a nonlinear elastic > > problem. This method is embedded in a Newmark implicit > > time integration. At the first several timestep the > > Newton iteration convergenced very well (10 steps). > > Did you see quadratic convergence? I agree with everything that Roy said. If it is not too much trouble, could you post the constitutive relations that you are using?. That is, (strain energy function (W), the second Piola-Kirchhoff tensor (S), and the material tangent modulus (C_{IJKL}). I ask this just to make sure that you are assembling the right consistent tangent matrix. -Nachiket. > The first thing you ought to check > if Newton's method is behaving oddly is whether you get quadratic > convergence as you approach the root - if not, then (assuming your > linear solves are accurate enough) your Jacobian (i.e. your system > matrix, not the geometric Jacobians) is probably inconsistent with > your residual function. If that happens, your iteration can still > converge, but the region of convergence may be smaller. > > Other possible problems: > > You may be starting from a bad initial guess. This has happened to me > before, when I left junk in a solution vector. Depending on whether > you're solving for the next timestep's solution or for the > delta_solution, a relatively safe initial guess might be the previous > timestep's solution or zero. > > The nonlinearities in your problem may be so bad that the region of > covnergence is too small for you to hit with your initial guess. In > that case you'll want to use a slower but safer method (successive > approximation, perhaps, or continuation) to get close to the root > followed by Newton to eliminate the last of your error. > > > The error could be numerical calculation of inversing matrix, > > because I used simple Gauss elimination. I will apply the method of > > Petsc. > > We've had some problems before with LASPACK not converging, but Gauss > elimination isn't one of them - I often switch to complete LU > factorization as a preconditioner when I'm trying to make sure that > the linear solver isn't causing me problems. Gauss is bad because > it's slow, not because it's inaccurate. > --- > Roy Stogner > > > ------------------------------------------------------- > This SF.net email is sponsored by: Splunk Inc. Do you grep through log files > for problems? Stop! Download the new AJAX search engine that makes > searching your log files as easy as surfing the web. DOWNLOAD SPLUNK! > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users -- ```
 Re: [Libmesh-users] error in newton iteration From: li pan - 2005-12-22 17:58:54 ```Hi Nachiket, Hey Nachiket, I implemented the algorithm of K.J.Bathe from his book << Finite element method >>, chapter 6, 1990. The algorithm is called Total Lagrange Formulation. I haven't calculated material tangent modulus. Because I only need stiffness matrix and second Piolar stress tensor. There must be something wrong in my implemented algorithm. I have to check it. Or you could give me some advice. I'm trying to implement an algorithm for large deformation, which fill the condition of Visco-elasticity. best pan --- Nachiket Gokhale wrote: > On Wed, 2005-12-21 at 12:38 -0600, Roy Stogner > wrote: > > On Wed, 21 Dec 2005, li pan wrote: > > > > > I used Newton iteration to solve a nonlinear > elastic > > > problem. This method is embedded in a Newmark > implicit > > > time integration. At the first several timestep > the > > > Newton iteration convergenced very well (10 > steps). > > > > Did you see quadratic convergence? > > I agree with everything that Roy said. > > If it is not too much trouble, could you post the > constitutive relations > that you are using?. That is, (strain energy > function (W), the second > Piola-Kirchhoff tensor (S), and the material tangent > modulus (C_{IJKL}). > I ask this just to make sure that you are assembling > the right > consistent tangent matrix. > > -Nachiket. > > > > > > > > The first thing you ought to check > > if Newton's method is behaving oddly is whether > you get quadratic > > convergence as you approach the root - if not, > then (assuming your > > linear solves are accurate enough) your Jacobian > (i.e. your system > > matrix, not the geometric Jacobians) is probably > inconsistent with > > your residual function. If that happens, your > iteration can still > > converge, but the region of convergence may be > smaller. > > > > Other possible problems: > > > > You may be starting from a bad initial guess. > This has happened to me > > before, when I left junk in a solution vector. > Depending on whether > > you're solving for the next timestep's solution or > for the > > delta_solution, a relatively safe initial guess > might be the previous > > timestep's solution or zero. > > > > The nonlinearities in your problem may be so bad > that the region of > > covnergence is too small for you to hit with your > initial guess. In > > that case you'll want to use a slower but safer > method (successive > > approximation, perhaps, or continuation) to get > close to the root > > followed by Newton to eliminate the last of your > error. > > > > > The error could be numerical calculation of > inversing matrix, > > > because I used simple Gauss elimination. I will > apply the method of > > > Petsc. > > > > We've had some problems before with LASPACK not > converging, but Gauss > > elimination isn't one of them - I often switch to > complete LU > > factorization as a preconditioner when I'm trying > to make sure that > > the linear solver isn't causing me problems. > Gauss is bad because > > it's slow, not because it's inaccurate. > > --- > > Roy Stogner > > > > > > > ------------------------------------------------------- > > This SF.net email is sponsored by: Splunk Inc. Do > you grep through log files > > for problems? Stop! Download the new AJAX search > engine that makes > > searching your log files as easy as surfing the > web. DOWNLOAD SPLUNK! > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > _______________________________________________ > > Libmesh-users mailing list > > Libmesh-users@... > > > https://lists.sourceforge.net/lists/listinfo/libmesh-users > -- > > > > > ------------------------------------------------------- > This SF.net email is sponsored by: Splunk Inc. Do > you grep through log files > for problems? Stop! Download the new AJAX search > engine that makes > searching your log files as easy as surfing the > web. DOWNLOAD SPLUNK! > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ```
 Re: [Libmesh-users] error in newton iteration From: Nachiket Gokhale - 2005-12-26 18:57:32 ```On Thu, 2005-12-22 at 09:58 -0800, li pan wrote: > Hi Nachiket, > Hey Nachiket, > I implemented the algorithm of K.J.Bathe from his book > << Finite element method >>, chapter 6, 1990. The > algorithm is called Total Lagrange Formulation. I > haven't calculated material tangent > modulus. Because I only need stiffness matrix and > second Piolar stress tensor. There must be something > wrong in my implemented algorithm. I have to check it. > Or you could give me some advice. I'm trying to > implement an algorithm for large deformation, which > fill the condition of Visco-elasticity. Hi Pan, As I understand the Total Lagrange formulation, the equations of elasticity (or for that matter viscoelasticity) are solved in the reference configuration. To solve them, one needs to linearize them, since they are non-linear equations. This linearization requires the calculation of the material tangent modulus. -Nachiket. > > best > > pan > > --- Nachiket Gokhale wrote: > > > On Wed, 2005-12-21 at 12:38 -0600, Roy Stogner > > wrote: > > > On Wed, 21 Dec 2005, li pan wrote: > > > > > > > I used Newton iteration to solve a nonlinear > > elastic > > > > problem. This method is embedded in a Newmark > > implicit > > > > time integration. At the first several timestep > > the > > > > Newton iteration convergenced very well (10 > > steps). > > > > > > Did you see quadratic convergence? > > > > I agree with everything that Roy said. > > > > If it is not too much trouble, could you post the > > constitutive relations > > that you are using?. That is, (strain energy > > function (W), the second > > Piola-Kirchhoff tensor (S), and the material tangent > > modulus (C_{IJKL}). > > I ask this just to make sure that you are assembling > > the right > > consistent tangent matrix. > > > > -Nachiket. > > > > > > > > > > > > > > > The first thing you ought to check > > > if Newton's method is behaving oddly is whether > > you get quadratic > > > convergence as you approach the root - if not, > > then (assuming your > > > linear solves are accurate enough) your Jacobian > > (i.e. your system > > > matrix, not the geometric Jacobians) is probably > > inconsistent with > > > your residual function. If that happens, your > > iteration can still > > > converge, but the region of convergence may be > > smaller. > > > > > > Other possible problems: > > > > > > You may be starting from a bad initial guess. > > This has happened to me > > > before, when I left junk in a solution vector. > > Depending on whether > > > you're solving for the next timestep's solution or > > for the > > > delta_solution, a relatively safe initial guess > > might be the previous > > > timestep's solution or zero. > > > > > > The nonlinearities in your problem may be so bad > > that the region of > > > covnergence is too small for you to hit with your > > initial guess. In > > > that case you'll want to use a slower but safer > > method (successive > > > approximation, perhaps, or continuation) to get > > close to the root > > > followed by Newton to eliminate the last of your > > error. > > > > > > > The error could be numerical calculation of > > inversing matrix, > > > > because I used simple Gauss elimination. I will > > apply the method of > > > > Petsc. > > > > > > We've had some problems before with LASPACK not > > converging, but Gauss > > > elimination isn't one of them - I often switch to > > complete LU > > > factorization as a preconditioner when I'm trying > > to make sure that > > > the linear solver isn't causing me problems. > > Gauss is bad because > > > it's slow, not because it's inaccurate. > > > --- > > > Roy Stogner > > > > > > > > > > > > ------------------------------------------------------- > > > This SF.net email is sponsored by: Splunk Inc. Do > > you grep through log files > > > for problems? Stop! Download the new AJAX search > > engine that makes > > > searching your log files as easy as surfing the > > web. DOWNLOAD SPLUNK! > > > > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > > _______________________________________________ > > > Libmesh-users mailing list > > > Libmesh-users@... > > > > > > https://lists.sourceforge.net/lists/listinfo/libmesh-users > > -- > > > > > > > > > > > ------------------------------------------------------- > > This SF.net email is sponsored by: Splunk Inc. Do > > you grep through log files > > for problems? Stop! Download the new AJAX search > > engine that makes > > searching your log files as easy as surfing the > > web. DOWNLOAD SPLUNK! > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > _______________________________________________ > > Libmesh-users mailing list > > Libmesh-users@... > > > https://lists.sourceforge.net/lists/listinfo/libmesh-users > > > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com > > > ------------------------------------------------------- > This SF.net email is sponsored by: Splunk Inc. Do you grep through log files > for problems? Stop! Download the new AJAX search engine that makes > searching your log files as easy as surfing the web. DOWNLOAD SPLUNK! > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > _______________________________________________ > Libmesh-users mailing list > Libmesh-users@... > https://lists.sourceforge.net/lists/listinfo/libmesh-users -- Nachiket Gokhale, Ph.D. Candidate (Mechanical Engg), Department of Aerospace and Mechanical Engineering Boston University, Boston, MA. Cell: 617-372-0637 email: gokhalen@... ```
 Re: [Libmesh-users] error in newton iteration From: li pan - 2005-12-27 11:55:17 ```Hi Nachiket, I think, you don't need to calculate material elasticity tensor Cijkl in every case. In some large deformation problems, you can calculate second Piolar stress through partial deviation of a reasonable energy function. best pan --- Nachiket Gokhale wrote: > On Thu, 2005-12-22 at 09:58 -0800, li pan wrote: > > Hi Nachiket, > > Hey Nachiket, > > I implemented the algorithm of K.J.Bathe from his > book > > << Finite element method >>, chapter 6, 1990. The > > algorithm is called Total Lagrange Formulation. I > > haven't calculated material tangent > > modulus. Because I only need stiffness matrix and > > second Piolar stress tensor. There must be > something > > wrong in my implemented algorithm. I have to check > it. > > Or you could give me some advice. I'm trying to > > implement an algorithm for large deformation, > which > > fill the condition of Visco-elasticity. > > Hi Pan, > > As I understand the Total Lagrange formulation, the > equations of > elasticity (or for that matter viscoelasticity) are > solved in the > reference configuration. To solve them, one needs to > linearize them, > since they are non-linear equations. This > linearization requires the > calculation of the material tangent modulus. > > -Nachiket. > > > > > > > best > > > > pan > > > > --- Nachiket Gokhale wrote: > > > > > On Wed, 2005-12-21 at 12:38 -0600, Roy Stogner > > > wrote: > > > > On Wed, 21 Dec 2005, li pan wrote: > > > > > > > > > I used Newton iteration to solve a nonlinear > > > elastic > > > > > problem. This method is embedded in a > Newmark > > > implicit > > > > > time integration. At the first several > timestep > > > the > > > > > Newton iteration convergenced very well (10 > > > steps). > > > > > > > > Did you see quadratic convergence? > > > > > > I agree with everything that Roy said. > > > > > > If it is not too much trouble, could you post > the > > > constitutive relations > > > that you are using?. That is, (strain energy > > > function (W), the second > > > Piola-Kirchhoff tensor (S), and the material > tangent > > > modulus (C_{IJKL}). > > > I ask this just to make sure that you are > assembling > > > the right > > > consistent tangent matrix. > > > > > > -Nachiket. > > > > > > > > > > > > > > > > > > > > > > The first thing you ought to check > > > > if Newton's method is behaving oddly is > whether > > > you get quadratic > > > > convergence as you approach the root - if not, > > > then (assuming your > > > > linear solves are accurate enough) your > Jacobian > > > (i.e. your system > > > > matrix, not the geometric Jacobians) is > probably > > > inconsistent with > > > > your residual function. If that happens, your > > > iteration can still > > > > converge, but the region of convergence may be > > > smaller. > > > > > > > > Other possible problems: > > > > > > > > You may be starting from a bad initial guess. > > > This has happened to me > > > > before, when I left junk in a solution vector. > > > > Depending on whether > > > > you're solving for the next timestep's > solution or > > > for the > > > > delta_solution, a relatively safe initial > guess > > > might be the previous > > > > timestep's solution or zero. > > > > > > > > The nonlinearities in your problem may be so > bad > > > that the region of > > > > covnergence is too small for you to hit with > your > > > initial guess. In > > > > that case you'll want to use a slower but > safer > > > method (successive > > > > approximation, perhaps, or continuation) to > get > > > close to the root > > > > followed by Newton to eliminate the last of > your > > > error. > > > > > > > > > The error could be numerical calculation of > > > inversing matrix, > > > > > because I used simple Gauss elimination. I > will > > > apply the method of > > > > > Petsc. > > > > > > > > We've had some problems before with LASPACK > not > > > converging, but Gauss > > > > elimination isn't one of them - I often switch > to > > > complete LU > > > > factorization as a preconditioner when I'm > trying > > > to make sure that > > > > the linear solver isn't causing me problems. > > > Gauss is bad because > > > > it's slow, not because it's inaccurate. > > > > --- > > > > Roy Stogner > > > > > > > > > > > > > > > > > > ------------------------------------------------------- > > > > This SF.net email is sponsored by: Splunk Inc. > Do > > > you grep through log files > > > > for problems? Stop! Download the new AJAX > search > > > engine that makes > > > > searching your log files as easy as surfing > the > > > web. DOWNLOAD SPLUNK! > > > > > > > > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > > > > _______________________________________________ > > > > Libmesh-users mailing list > > > > Libmesh-users@... > > > > > > > > > > https://lists.sourceforge.net/lists/listinfo/libmesh-users > > > -- > > > > > > > > > > > > > > > > > > ------------------------------------------------------- > > > This SF.net email is sponsored by: Splunk Inc. > Do > > > you grep through log files > > > for problems? Stop! Download the new AJAX > search > > > engine that makes > > > searching your log files as easy as surfing the > > > web. DOWNLOAD SPLUNK! > > > > > > http://ads.osdn.com/?ad_id=7637&alloc_id=16865&op=click > > > _______________________________________________ > > > Libmesh-users mailing list > > > Libmesh-users@... > > > > > > https://lists.sourceforge.net/lists/listinfo/libmesh-users > === message truncated === __________________________________ Yahoo! for Good - Make a difference this year. http://brand.yahoo.com/cybergivingweek2005/ ```