polyfem · maxpaik16 · Feb 26, 2026 · Apr 6, 2026
diff --git a/README.md b/README.md
@@ -17,5 +17,72 @@ This repository contains the scripts to regenerate the figures in the paper:
 }
 ```
 
-This branch contains updated scripts. For the original check the [original](https://github.com/polyfem/Decoupling-Simulation-Accuracy-from-Mesh-Quality/tree/original) branch.
+### Python teaser
 
+We created a simple [jupyter notebook](https://raw.githubusercontent.com/polyfem/Decoupling-Simulation-Accuracy-from-Mesh-Quality/master/Decoupling-Simulation-Accuracy-from-Mesh-Quality.ipynb) with an example to run the teaser image.
+
+This notebook can be interactively run with binder!
+[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/polyfem/Decoupling-Simulation-Accuracy-from-Mesh-Quality.git/master?filepath=Decoupling-Simulation-Accuracy-from-Mesh-Quality.ipynb)
+
+### Dependencies
+
+##### PolyFEM
+
+A specific version of [PolyFEM](https://github.com/polyfem/polyfem) is included as a submodule. To retrieve and compile it, run the following commands:
+
+```
+git submodule update --init --recursive
+cd polyfem
+mkdir build
+cd build
+cmake ..
+make -j 8
+```
+
+Make sure that [PARDISO](https://www.pardiso-project.org/) is found and enabled, otherwise you might not be able to generate certain figures (see below). In PolyFEM, `FindPardiso.cmake` will look for the PARDISO library in `~/.local` or `~/.pardiso`. If you installed PARDISO in a different location, you may need to update this file accordingly.
+
+##### Conda Environment
+
+Install [Miniconda](https://docs.conda.io/en/latest/miniconda.html) for Python 3, and create the environment for this paper from the `conda.yml` file:
+
+```
+conda env create -f conda.yml
+```
+
+##### PyRenderer (via Singularity/Docker)
+
+[PyRenderer](https://github.com/qnzhou/PyRenderer) is used to render the images in the paper. PyRenderer is a wrapper around [Mitsuba](https://github.com/mitsuba-renderer/mitsuba), and as such is a bit complicated to setup.
+There is a [Docker image](https://hub.docker.com/r/qnzhou/pyrender) available on Docker-Hub.
+We also provide a pre-built Singularity [Singularity](https://www.sylabs.io) image (>=v3.0.0) of PyRenderer. Singularity is similar to Docker, but does not require root privilege in order to run images. Please read the [documentation](https://sylabs.io/guides/3.3/user-guide/) to install it on your machine.
+
+- <details><summary>Our Singularity image can be downloaded programmatically from our Google Drive using `gdown` (click to expand).</summary><p>
+```
+pip3 install --user gdown
+gdown "https://drive.google.com/uc?id=1zfqiThhSRZkmNDeaXj2nGC1kf00kRIsK"
+md5sum pyrenderer.sif
+# 557ce7496b29fd11d0808f5ec918a995
+```
+</p></details>
+
+- For docker users, make sure to:
+    1. [Install Docker](https://docs.docker.com/install/linux/docker-ce/ubuntu/) following official instructions.
+    2. [Allow](https://docs.docker.com/install/linux/linux-postinstall/) to run docker as a non-root user.
+
+### Solver
+
+As stated in the paper, we use [PARDISO](https://www.pardiso-project.org/) for the following figures:
+- Figure 7
+- Figure 8
+- Figure 11
+- Figure 21
+- Table 1
+
+And [HYPRE](https://computing.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods) for the following figures:
+- Figure 9
+- Figure 10
+- Figure 16
+- Figure 17
+- Figure 20
+
+
+If you try to generate the first figures with an iterative solver, running times may be exceedingly long, so it is not recommended.
diff --git a/bridge/large_angle_strip_0.json b/bridge/large_angle_strip_0.json
@@ -25,5 +25,24 @@
         "err_lp": 0.019251172364018153,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_1.json b/bridge/large_angle_strip_1.json
@@ -25,5 +25,24 @@
         "err_lp": 0.023046469357049414,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_2.json b/bridge/large_angle_strip_2.json
@@ -25,5 +25,24 @@
         "err_lp": 0.018236384619905614,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_3.json b/bridge/large_angle_strip_3.json
@@ -25,5 +25,24 @@
         "err_lp": 0.018232285249566823,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_4.json b/bridge/large_angle_strip_4.json
@@ -25,5 +25,24 @@
         "err_lp": 0.018231336446474202,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_5.json b/bridge/large_angle_strip_5.json
@@ -25,5 +25,24 @@
         "err_lp": 0.01823195894247403,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_6.json b/bridge/large_angle_strip_6.json
@@ -25,5 +25,24 @@
         "err_lp": 0.018231258884821137,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_7.json b/bridge/large_angle_strip_7.json
@@ -25,5 +25,24 @@
         "err_lp": 0.018230633203504775,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_8.json b/bridge/large_angle_strip_8.json
@@ -25,5 +25,24 @@
         "err_lp": 0.018230024632425103,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/bridge/large_angle_strip_8_no.json b/bridge/large_angle_strip_8_no.json
@@ -25,5 +25,24 @@
         "err_lp": 0.4788283491724556,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/common.json b/common.json
@@ -2,6 +2,13 @@
     "solver": {
         "linear": {
             "solver": "Eigen::SimplicialLDLT"
+        },
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean"
         }
     },
     "output": {

diff --git a/main/conditioning_44000_bad.json b/main/conditioning_44000_bad.json
@@ -25,5 +25,24 @@
         "err_lp": 0.4715054370582474,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }
diff --git a/main/conditioning_44000_good.json b/main/conditioning_44000_good.json
@@ -25,5 +25,24 @@
         "err_lp": 0.47378407647641807,
         "margin": 1e-05,
         "time_steps": "static"
+    },
+    "solver": {
+        "advanced": {
+            "characteristic_force_density": 1,
+            "characteristic_length": 1
+        },
+        "nonlinear": {
+            "norm_type": "Euclidean",
+            "first_grad_norm_tol": 1e-10,
+            "grad_norm_tol": 1e-08,
+            "x_delta_tol": 0,
+            "advanced": {
+                "f_delta_tol": 0,
+                "derivative_along_delta_x_tol": 0
+            },
+            "line_search": {
+                "use_grad_norm_tol": 1e-06
+            }
+        }
     }
 }