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Why does my newton-Raphson iteration fail?
$begingroup$
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
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
$endgroup$
add a comment |
$begingroup$
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
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
$endgroup$
add a comment |
$begingroup$
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
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
$endgroup$
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
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
asked Jan 20 at 14:52
Msen RezaeeMsen Rezaee
306312
306312
add a comment |
add a comment |
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