Why does my newton-Raphson iteration fail?












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Suppose that I have the following energy equation that is a function of $varepsilon$, the strain, and $eta$, the hardening parameter.



$phi=frac{1}{2}E varepsilon_e^2+frac{1}{2}H eta^2$, $qquad varepsilon_e=varepsilon-eta epsilon_t$



where $E$ and $H$ are, respectively, the elasticity and hardening parameter, $varepsilon_e$ is the elastic part of strain and $epsilon_t$ is a constant.



Applying the Newton-Raphson iterative solver in a monolithic manner I obtain the residual, $R$ and the tangent matrix $A$ and the solutions at a given time.



Everything goes well when $H>0$ and the procedure has quadratic convergence at each step. But, as soon as I put $H=0$, the procedure fails to converge. So in order to circumvent this issue, I have to take a small value for $H$, something like $H=0.001.$



Can anyone explain why this happens? I mean why $H=0$ makes the problem ill-posed?






convergence problem-solving newton-raphson finite-element-method







share|cite|improve this question









$endgroup$

















    0












    $begingroup$


    Suppose that I have the following energy equation that is a function of $varepsilon$, the strain, and $eta$, the hardening parameter.



    $phi=frac{1}{2}E varepsilon_e^2+frac{1}{2}H eta^2$, $qquad varepsilon_e=varepsilon-eta epsilon_t$



    where $E$ and $H$ are, respectively, the elasticity and hardening parameter, $varepsilon_e$ is the elastic part of strain and $epsilon_t$ is a constant.



    Applying the Newton-Raphson iterative solver in a monolithic manner I obtain the residual, $R$ and the tangent matrix $A$ and the solutions at a given time.



    Everything goes well when $H>0$ and the procedure has quadratic convergence at each step. But, as soon as I put $H=0$, the procedure fails to converge. So in order to circumvent this issue, I have to take a small value for $H$, something like $H=0.001.$



    Can anyone explain why this happens? I mean why $H=0$ makes the problem ill-posed?






    convergence problem-solving newton-raphson finite-element-method







    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      Suppose that I have the following energy equation that is a function of $varepsilon$, the strain, and $eta$, the hardening parameter.



      $phi=frac{1}{2}E varepsilon_e^2+frac{1}{2}H eta^2$, $qquad varepsilon_e=varepsilon-eta epsilon_t$



      where $E$ and $H$ are, respectively, the elasticity and hardening parameter, $varepsilon_e$ is the elastic part of strain and $epsilon_t$ is a constant.



      Applying the Newton-Raphson iterative solver in a monolithic manner I obtain the residual, $R$ and the tangent matrix $A$ and the solutions at a given time.



      Everything goes well when $H>0$ and the procedure has quadratic convergence at each step. But, as soon as I put $H=0$, the procedure fails to converge. So in order to circumvent this issue, I have to take a small value for $H$, something like $H=0.001.$



      Can anyone explain why this happens? I mean why $H=0$ makes the problem ill-posed?






      convergence problem-solving newton-raphson finite-element-method







      share|cite|improve this question









      $endgroup$




      Suppose that I have the following energy equation that is a function of $varepsilon$, the strain, and $eta$, the hardening parameter.



      $phi=frac{1}{2}E varepsilon_e^2+frac{1}{2}H eta^2$, $qquad varepsilon_e=varepsilon-eta epsilon_t$



      where $E$ and $H$ are, respectively, the elasticity and hardening parameter, $varepsilon_e$ is the elastic part of strain and $epsilon_t$ is a constant.



      Applying the Newton-Raphson iterative solver in a monolithic manner I obtain the residual, $R$ and the tangent matrix $A$ and the solutions at a given time.



      Everything goes well when $H>0$ and the procedure has quadratic convergence at each step. But, as soon as I put $H=0$, the procedure fails to converge. So in order to circumvent this issue, I have to take a small value for $H$, something like $H=0.001.$



      Can anyone explain why this happens? I mean why $H=0$ makes the problem ill-posed?






      convergence problem-solving newton-raphson finite-element-method




      convergence problem-solving newton-raphson finite-element-method






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 20 at 14:52









      Msen RezaeeMsen Rezaee

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