{ "cells": [ { "cell_type": "markdown", "id": "e49a05a6-e630-4321-8739-1149122cb4fd", "metadata": {}, "source": [ "# Solving a Laplace transmission problem with the Multiple Traces Formulation" ] }, { "cell_type": "markdown", "id": "b928991c-05bc-4a5a-92cf-3bb167abfe1a", "metadata": {}, "source": [ "## Geometry" ] }, { "cell_type": "markdown", "id": "22ff097e-aab4-44a6-828a-fc01dca25671", "metadata": {}, "source": [ "We consider $N$ disjoint spheres in $\\mathbb{R}^3$, with the following notation:\n", "- Position vectors of the sphere centers: $\\mathbf{p_j} \\in \\mathbb{R}^3$, with $j \\in \\{1, ..., N\\}$.\n", "- Radii: $\\tilde{r}_j \\in \\mathbb{R}^+$, with $j \\in \\{1, ..., N\\}$.\n", "- Interior of sphere $j$: $\\Omega_j$, with $j \\in \\{1, ..., N\\}$.\n", "- Boundary of sphere $j$: $\\Gamma_j := \\partial \\Omega_j$.\n", "- Exterior medium: $\\Omega_0$, defined as $\\mathbb{R}^3$ without the spheres and their boundaries." ] }, { "cell_type": "markdown", "id": "06e10668-c599-468e-a56c-8411caa71cc8", "metadata": {}, "source": [ "## Volume problem" ] }, { "cell_type": "markdown", "id": "1e8fbe6d-da9f-4f86-ab82-799e4f35f3e4", "metadata": {}, "source": [ "We want to find $u_j \\in H^1_{loc}(\\Omega_j)$, $j \\{0, ..., N \\}$, such that they solve:\n", "$$\\text{div} (\\sigma_j \\nabla u_j) = 0 \\quad \\text{ in } \\Omega_j, \\text{ with } j \\in \\{0, ..., N \\},$$\n", "$$-\\gamma_d^{0j} u_0 + \\gamma_d^{j} u_j = \\gamma_d^{0j} \\phi_e \\quad \\text{ on } \\Gamma_j, \\text{ with } j \\in \\{1, ..., N \\},$$\n", "$$\\sigma_0 \\gamma_n^{0j} u_0 + \\sigma_j \\gamma_n^{j} u_j = - \\sigma_0\\gamma_n^{0j} \\phi_e \\quad \\text{ on } \\Gamma_j, \\text{ with } j \\in \\{1, ..., N \\},$$\n", "$$\\lim_{||\\mathbf{x}||_2 \\rightarrow \\infty} u_0(\\mathbf{x}) = \\mathcal{O}\\left(\\frac{1}{||\\mathbf{x}||_2}\\right),$$" ] }, { "cell_type": "markdown", "id": "d3849c39-ed5f-4d19-b5ad-52ae6ca4fb03", "metadata": {}, "source": [ "with\n", "$$\\gamma_d^{0j} u_0 := u_0|_{\\Gamma_j},$$\n", "$$\\gamma_d^{j} u_j := u_j|_{\\Gamma_j},$$\n", "$$\\gamma_n^{0j} u_0 := \\nabla u_0|_{\\Gamma_j} \\cdot \\widehat{n}_{0j},$$\n", "$$\\gamma_n^{j} u_j := \\nabla u_j|_{\\Gamma_j}\\cdot \\widehat{n}_{j},$$\n", "where $\\widehat{n}_{j}$ is the exterior normal of $\\Omega_j$, with $j\\in \\{ 1, ..., N\\}$ and $\\widehat{n}_{0j}=-\\widehat{n}_{j}$." ] }, { "cell_type": "markdown", "id": "b337872b-2e29-4a8e-b176-c349f0375260", "metadata": {}, "source": [ "$\\sigma_j$, with $j\\in \\{ 1, ..., N\\}$, are positive parameters and\n", "$$\\phi_e(\\mathbf{x}) = \\frac{1}{4 \\pi \\sigma_0 ||\\mathbf{x} - \\mathbf{p}||_2},$$\n", "with $\\mathbf{p} \\in \\Omega_0$." ] }, { "cell_type": "markdown", "id": "87304d5d-7e4f-4162-b0ef-a86a073cd6d6", "metadata": {}, "source": [ "## Boundary formulation" ] }, { "cell_type": "markdown", "id": "a5e227e9-299a-4017-982d-46d9c45a93a0", "metadata": {}, "source": [ "### Free space fundamental solution for the Laplace equation" ] }, { "cell_type": "markdown", "id": "cba97fb9-f21d-49e9-8a69-c8c57e75b856", "metadata": {}, "source": [ "The free space fundamental solution of the Laplace equation, which satisfies the radiation condition is:\n", "$$g\\left(\\mathbf{r},\\mathbf{r'}\\right):= \\frac{1}{4\\pi ||\\mathbf{r}-\\mathbf{r}'||_2}, \\quad \\text{with } \\mathbf{r}\\not = \\mathbf{r'}, \\quad \\text{and } -\\Delta g \\left(\\mathbf{r},\\mathbf{r'}\\right)=\\delta \\left(\\mathbf{r}-\\mathbf{r'}\\right).$$" ] }, { "cell_type": "markdown", "id": "fcba8fc2-2abc-47f5-b029-812f3ac3170f", "metadata": {}, "source": [ "### Layer operators" ] }, { "cell_type": "markdown", "id": "63f3d615-c064-4da1-a9a5-29e548486dec", "metadata": {}, "source": [ "Single and double layer operators defined for smooth densities:\n", "$$DL_{0j} \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} \\psi\\left(\\mathbf{r}'\\right) \\nabla g\\left(\\mathbf{r},\\mathbf{r'}\\right) \\cdot \\widehat{\\mathbf{n}}_{0j} \\ dS',$$\n", "$$SL_{0j} \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} {\\psi\\left(\\mathbf{r}'\\right) g\\left(\\mathbf{r},\\mathbf{r'}\\right) dS'},$$\n", "$$DL_j \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} {\\psi\\left(\\mathbf{r}'\\right) \\nabla g\\left(\\mathbf{r},\\mathbf{r'}\\right) \\cdot \\widehat{\\mathbf{n}}_{j} \\ dS'},$$\n", "$$SL_j \\left(\\psi\\right)\\left(\\mathbf{r}\\right):=\\int_{\\Gamma_j} {\\psi\\left(\\mathbf{r}' \\right) g\\left(\\mathbf{r},\\mathbf{r'}\\right) dS'}$$\n", "\n", "with the gradient being taken with respect to $\\mathbf{r}'$, $\\widehat{\\mathbf{n}}_j$ being the exterior normal vector of $\\Omega_j$, and $\\widehat{\\mathbf{n}}_j=-\\widehat{\\mathbf{n}}_{0j}$.\n", "\n", "These operators are linear and continuous in the following Sobolev spaces:\n", "$$DL_{0j}: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^1_{loc} \\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right),$$\n", "$$SL_{0j}: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^1_{loc} \\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right) , $$\n", "$$DL_{j}: H^{\\frac{1}{2}}(\\Gamma_j)\\rightarrow H^1_{loc} \\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right),$$\n", "$$SL_{j}: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^1_{loc}\\left(\\mathbb{R}^3 \\setminus \\cup_{j=1}^{N}\\Gamma_j\\right).$$" ] }, { "cell_type": "markdown", "id": "1a08a548-252e-4eab-b24f-3f1b6d9eadf0", "metadata": {}, "source": [ "### Representation formula" ] }, { "cell_type": "markdown", "id": "5244183c-1c9a-45f8-a3a9-c5d445a8b47c", "metadata": {}, "source": [ "The integral representation formulas for $u_j \\in H^1(\\Omega_j)$, $u_0 \\in H^1_{loc}(\\Omega_0)$ read\n", "$$\\begin{aligned}\n", " u_0 &= - \\sum_{j=1}^N DL_{0j} \\left(\\gamma_d^{0j} u_0 \\right) + \\sum_{j=1}^N SL_{0j} \\left(\\gamma_n^{0j} u_0 \\right) ,\\\\\n", " u_j&=\t-DL_j \\left(\\gamma_d^{j} u_j \\right) +SL_j \\left(\\gamma_n{j} u_j \\right), \\quad \\forall j\\in \\{1, ..., N\\}.\n", "\\end{aligned}$$\n", "where $u_j$ are zero-valued on the complement of $\\Omega_j$." ] }, { "cell_type": "markdown", "id": "d299e756-a217-42b9-aa7a-ef76db9df2e5", "metadata": {}, "source": [ "### Boundary integral operators" ] }, { "cell_type": "markdown", "id": "3e240bb2-9f25-40d0-84e5-43650b7cc2b9", "metadata": {}, "source": [ "We recall the definition of the boundary integral operators:\n", "$$\\begin{aligned}\n", "\tV_{i,j}^0 &:= \\frac{1}{2} \\left( \\gamma_d^{i} SL_{0j} + \\gamma_d^{0i} SL_{0j} \\right) ,\n", "\t& V_{j}&:= \\frac{1}{2} \\left( \\gamma_d^{0j} SL_{j} + \\gamma_d^{j} SL_{j} \\right) ,\\\\\n", "\tK_{i,j}^0&:= \\frac{1}{2} \\left(\\gamma_d^{i} DL_{0j} + \\gamma_d^{0i} DL_{0j} \\right) ,\n", "\t&K_{j}&:= \\frac{1}{2} \\left(\\gamma_d^{0j} DL_{j} + \\gamma_d^{j} DL_{j} \\right),\\\\\n", "\tK^{*0}_{i,j}&:= \\frac{1}{2} \\left( - \\gamma_n ^{i} SL_{0j} + \\gamma_n ^{0i} SL_{0j} \\right),\n", "\t & K^{*}_{j} &:= \\frac{1}{2} \\left( -\\gamma_n ^{0j} SL_{j} + \\gamma_n ^{j} SL_{j} \\right), \\\\\n", "\tW_{i,j}^0 &:= -\\frac{1}{2} \\left( - \\gamma_n^{i} DL_{0j} + \\gamma_n^{0i} DL_{0j} \\right) ,\n", "\t& W_{j} &:=- \\frac{1}{2} \\left( -\\gamma_n^{0j} DL_{j} + \\gamma_n^{j} DL_{j} \\right).\n", "\\end{aligned}$$\n", "\n", "These operators are linear and continuous in the following Sobolev spaces: \n", "$$\\begin{aligned}\n", "\tV_{{i},j}^0 &: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_i),\n", "\t&V_{j}&: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_j),\\\\\n", "\tW_{{i},j}^0&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_i),\n", "\t&W_{j}&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_j) ,\\\\\n", "\tK_{{i},j}^0&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_i),\n", "\t&K_{j}&: H^{\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{\\frac{1}{2}}(\\Gamma_j) ,\\\\\n", "\tK^{*0}_{{i},j}&: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_i),\n", "\t&K^*_{j}&: H^{-\\frac{1}{2}}(\\Gamma_j) \\rightarrow H^{-\\frac{1}{2}}(\\Gamma_j).\n", "\\end{aligned}$$\n", "\n", "Since the domains are smooth, the jump relations for the potentials across a closed boundary yield\n", "$$\\begin{aligned}\n", "\tV_{{i},j}^0 &= \\gamma_d^{0{i}} SL_{0j},\n", "\t& V_{j}&= \\gamma_d^{j} SL_{j},\\\\\n", "\tW_{{i},j}^0 &=- \\gamma_n^{0{i}} DL_{0j},\n", "\t& W_{j} &=- \\gamma_n^{j} DL_{j}, \\\\\n", "\t K_{{i},j}^0&= \\gamma_d^{0{i}} DL_{0j}\\text{ with } {i} \\not=j,\n", "\t & K^{*0}_{{i},j} &= \\gamma_n ^{0{i}} SL_{0j}\\text{ with } {i} \\not=j,\n", "\\end{aligned}$$\n", "and\n", "$$\\begin{aligned}\n", "\tK_{j,j}^0(\\psi) &= \\frac{1}{2}\\psi +\\gamma_d^{0j} {DL_{0j}(\\psi)} ,\n", "\t&K_{j}(\\psi) &= \\frac{1}{2} \\psi +\\gamma_d^{j} {DL_{j}(\\psi)} ,\\\\\n", "\t K^{*0}_{j,j}(\\psi) &= -\\frac{1}{2} \\psi + \\gamma_n^{0j} {SL_{0j}(\\psi)},\n", "\t&K^*_{j}(\\psi) &= -\\frac{1}{2} \\psi + \\gamma_n^j {SL_{j}(\\psi)}.\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "8fd09825-853e-4efb-92e7-4ec9485124ee", "metadata": {}, "source": [ "### Multiple traces formulation" ] }, { "cell_type": "markdown", "id": "833a035e-c78b-44f5-a6a2-74fa744f89dc", "metadata": {}, "source": [ "For $j\\in \\{1,...,N\\}$, we introduce the Cartesian product of Hilbert spaces ${\\boldsymbol{H}_j} := H^{\\frac{1}{2}}(\\Gamma_j) \\times H^{-\\frac{1}{2}}(\\Gamma_j)$, with norm $\\|\\cdot \\|_{\\boldsymbol{H}_j}= \\|\\cdot \\|_{H^{\\frac{1}{2}}(\\Gamma_j)} + \\| \\cdot \\|_{H^{-\\frac{1}{2}}(\\Gamma_j)}$.\n", "\n", "Let be $\\boldsymbol{\\phi}$, $\\boldsymbol{\\xi}$ $\\in {\\boldsymbol{H}_j}$, such that $\\boldsymbol{\\phi} = (\\phi_D, \\phi_N )$ and $\\boldsymbol{\\xi} = (\\xi_D, \\xi_N )$. We introduce the cross-product over $\\Gamma_j$ (Section 2.2.1, HiptmairJerez2012) by $\\langle \\boldsymbol{\\phi}, \\boldsymbol{\\xi}\\rangle_{\\times,j} := \\langle \\phi_d, \\xi_n \\rangle_{j} + \\langle \\xi_d , \\phi_n\\rangle_{j},$ where for brevity we denote $\\langle \\xi_d , \\phi_n\\rangle_{j}$ := $\\langle \\xi_d, \\phi_n\\rangle_{H^{\\frac{1}{2}}(\\Gamma_j) \\times H^{-\\frac{1}{2}}(\\Gamma_j)}$." ] }, { "cell_type": "markdown", "id": "1b4295ae-a22a-4319-a5c4-79203c1137d0", "metadata": {}, "source": [ "We define also the flip-sign operator $\\mathsf{X}_j:{\\boldsymbol{H}_j}\\rightarrow {\\boldsymbol{H}_j}$, $\\gamma^{0j}:H^1_{loc}(\\Delta,\\Omega_0)\\rightarrow {\\boldsymbol{H}_j}$ and $\\gamma^{j}:H^1(\\Delta,\\Omega_j)\\rightarrow {\\boldsymbol{H}_j}$ as:\n", "$$\\mathsf{X}_j:=\t\\begin{bmatrix}\n", " \tI & 0 \\\\[2mm]\n", " \\displaystyle\n", " \t0 & -\\frac{\\sigma_0}{\\sigma_j} I\n", "\t\\end{bmatrix}, \\quad\n", "\t\\gamma^{0j} := \t\\begin{pmatrix}\n", " \t\\gamma_d^{0j} \\\\[2mm]\n", " \t\\gamma_n^{0j}\n", "\t\\end{pmatrix}\n", "\t\\quad \\text{ and } \\quad\n", "\t\\gamma^{j} := \t\\begin{pmatrix}\n", " \t\\gamma_d^{j} \\\\[2mm]\n", " \t\\gamma_n^{j}\n", "\t\\end{pmatrix},\\quad j \\in \\{1,..., N\\},$$\n", "with $I$ being the identity operator in the corresponding functional space, and for simplicity, we adopt the same notation for $I$ in different spaces." ] }, { "cell_type": "markdown", "id": "f72ca377-c071-44d9-aa21-6c8c35492591", "metadata": {}, "source": [ "Then, we write Dirichlet and Neumamn boundary conditions succinctly as\n", "$$\\begin{aligned}\n", "-\\mathsf{X}_j \\gamma^{0j} u_0+ \\gamma^j u_j &= \\mathsf{X}_j \\gamma^{0j} \\phi_e , \\\\\n", "\\gamma^{0j} u_0 -\\mathsf{X}_j^{-1}\\gamma^j u_j &=- \\gamma^{0j} \\phi_e,\t\n", "\\end{aligned}$$\n", "where both equations are equivalent." ] }, { "cell_type": "markdown", "id": "8388aa4c-3377-4359-9ad6-955e7ac0847e", "metadata": {}, "source": [ "Taking Dirichlet and Neumann traces of both representation formulas for $u_0$ and $u_j$, and rewriting in terms of BIOs, we obtain\n", "$$\\begin{aligned}\n", "\t\\gamma_d^{0j} u_0 &=\t-\\left(-\\frac{1}{2}I\\left(\\gamma_d^{0j} u_0 \\right)+\\sum_{i=1}^n K_{j,i}^0 \\left(\\gamma_d^{0i} u_0 \\right)\\right) +\\sum_{i=1}^n V_{j,i}^0 \\left(\\gamma_n^{0i} u_0 \\right),\\\\\n", "\t\\gamma_n^{0j} u_0 &=\t\\sum_{i=1}^n W_{j,i}^0 \\left(\\gamma_d^{0i} u_0 \\right) +\\left( \\frac{1}{2}I\\left(\\gamma_n^{0j} u_0 \\right)+\\sum_{i=1}^n K_{j,i}^{*0} \\left(\\gamma_n^{0i} u_0 \\right)\\right),\\\\\n", "\t\\gamma_d^{j} u_j &=\t-\\left(-\\frac{1}{2}I\\left(\\gamma_d^{j} u_j \\right) +K_j\\left(\\gamma_d^{j} u_j \\right) \\right) \n", "\t+V_j \\left(\\gamma_n^{j} u_j \\right),\\\\\n", "\t\\gamma_n^{j} u_j &=\tW_j \\left(\\gamma_d^{j} u_j \\right) +\\left( \\frac{1}{2}I\\left(\\gamma_n^{j} u_j \\right) + K^*_j\\left(\\gamma_n^{j} u_j \\right) \\right) .\n", "\\end{aligned}$$\n", "After some algebra, one can write\n", "$$\n", "\\gamma^{0j} u_0=\t2\\sum_{i=1}^N \\mathsf{A}_{j,i}^0 \\gamma^{0i}u_0, \\quad \\gamma^j u_j=\t2\\mathsf{A}_j \\gamma^j u_j, \\quad j \\in \\{1,...,N\\}, \n", "$$\n", "with $\\displaystyle \\mathsf{A}_{j,i}^0:=\t\\begin{bmatrix}\n", " \t-K_{j,i}^0 & V_{j,i}^0 \\\\\n", " \tW_{j,i}^0 & K_{j,i}^{*0} \\\\\n", "\t\\end{bmatrix} \\text{ and }\\mathsf{A}_j:=\t\\begin{bmatrix}\n", " \t-K_j & V_j \\\\\n", " \tW_j & K_j^* \\\\\n", "\t\\end{bmatrix}.$" ] }, { "cell_type": "markdown", "id": "b2015759-2e32-43cb-a68c-4a0ff22e7c63", "metadata": {}, "source": [ "By replacing $\\gamma^{0j} u_0$, $\\gamma^j u_j$ into the boundary conditions we obtain\n", "$$\\begin{aligned}\n", " 2\\sum_{i=1}^n \\mathsf{A}_{j,i}^0 \\gamma^{0{i}} u_0 \n", " -\\mathsf{X}_j^{-1}\\gamma^j u_j \n", " &= - \\gamma^{0j} \\phi_e ,\\\\\n", "\t-\\mathsf{X}_j\\gamma^{0j} u_0 +2\\mathsf{A}_j \\gamma^j u_j &= \\mathsf{X}_j \\gamma^{0j} \\phi_e \\quad \\text{ on } \\Gamma_j.\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "75486513-22ba-42df-8dea-78d917005f45", "metadata": {}, "source": [ "We define Cartesian product space of multiple traces $\\mathbb{H}:=\\Pi_{j=1}^N \\boldsymbol{H}_j$ and $\\mathbb{H}^{(2)} := \\mathbb{H} \\times \\mathbb{H} = \\Pi_{j=1}^N \\boldsymbol{H}_j \\times \\Pi_{j=1}^N \\boldsymbol{H}_j$, and the cross-product: $$\\displaystyle \\langle \\boldsymbol{\\phi}, \\boldsymbol{\\xi } \\rangle_{\\times} = \\sum_{j=1}^N \\langle \\boldsymbol{\\phi}^{0j}, \\boldsymbol{\\xi}^{0j} \\rangle_{\\times,j} + \\sum_{j=1}^N \\langle \\boldsymbol{\\phi}^{j}, \\boldsymbol{\\xi}^{j} \\rangle_{\\times,j},$$ with $\\boldsymbol{\\phi} = (\\boldsymbol{\\phi}^{01},..., \\boldsymbol{\\phi}^{0N}, \\boldsymbol{\\phi}^{1}, ..., \\boldsymbol{\\phi}^{N})$ and $\\boldsymbol{\\xi} = (\\boldsymbol{\\xi}^{01},..., \\boldsymbol{\\xi}^{0N}, \\boldsymbol{\\xi}^{1}, ..., \\boldsymbol{\\xi}^{N})$." ] }, { "cell_type": "markdown", "id": "71bce823-1f9c-45fe-9277-655a843a624c", "metadata": {}, "source": [ "Now, we can introduce the local Multiple Trace formulation (MTF) operator (Section 3.2.3, HiptmairJerez2012), $\\boldsymbol{\\mathsf{M}}_N: \\mathbb{H}^{(2)} \\rightarrow \\mathbb{H}^{(2)}$:\n", "$$\\begin{aligned}\n", "\t\\boldsymbol{\\mathsf{M}}_N:=\t\\begin{bmatrix}\n", " 2\\boldsymbol{\\mathsf{A}}_{0,N} & -\\boldsymbol{\\mathsf{X}}_N^{-1} \\\\\n", " -\\boldsymbol{\\mathsf{X}}_{N} & 2\\boldsymbol{\\mathsf{A}}_{1,N}\n", "\t\\end{bmatrix}, \\text{ with } \\boldsymbol{\\mathsf{A}}_{0,N}:=\\begin{bmatrix}\n", " \t\\mathsf{A}_{1,1}^0 & \\mathsf{A}_{1,2}^0 & ... & \\mathsf{A}_{1,N}^0\\\\\n", " \t\\mathsf{A}_{2,1}^0 & \\mathsf{A}_{2,2}^0 & ... & \\mathsf{A}_{2,N}^0\\\\\n", " \t\\vdots & &\\ddots & \\vdots\\\\\n", " \t\\mathsf{A}_{N,1}^0 & \\mathsf{A}_{N,2}^0 & ... & \\mathsf{A}_{N,N}^0\n", "\t\\end{bmatrix},\n", "\\end{aligned}$$\n", "$$\\begin{aligned}\n", "\t&\\boldsymbol{\\mathsf{A}}_{1,N}:=\\begin{bmatrix}\n", " \t\\mathsf{A}_{1} & 0 & ... & 0\\\\\n", " \t0 & \\mathsf{A}_{2} & ... & 0\\\\\n", " \t\\vdots & &\\ddots & \\vdots\\\\\n", " \t0 & ... & 0& \\mathsf{A}_N\\\\\n", "\t\\end{bmatrix} \\text{ and } \\boldsymbol{\\mathsf{X}}_N:=\\begin{bmatrix}\n", " \t\\mathsf{X}_{1} & 0 & ... & 0\\\\\n", " \t0 & \\mathsf{X}_{2} & ... & 0\\\\\n", " \t\\vdots & &\\ddots & \\vdots\\\\\n", " \t0 & ... & 0& \\mathsf{X}_N\n", "\t\\end{bmatrix}. \n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "aaed9cf7-ddbc-48aa-a322-8abed35c3ba5", "metadata": {}, "source": [ "With the MTF operator, the transmission problem can be written as:\n", "$$\\begin{aligned}\n", "\t\\boldsymbol{\\mathsf{M}}_N\\begin{pmatrix} \\gamma^0_u \\\\\t \\gamma_u \\end{pmatrix} = \\begin{pmatrix} -\\gamma^0_{\\phi_e} \\\\ \\boldsymbol{\\mathsf{X}}_N \\gamma^0_{\\phi_e}\t\\end{pmatrix},\n", "\\end{aligned}$$\n", "where we use the notation:\n", "$$\\begin{aligned}\n", "\t\\gamma^0_u &:=\\begin{pmatrix} \\gamma^{01} u_0, \\gamma^{02} u_0, ..., \\gamma^{0N} u_0 \\end{pmatrix}^t , &\\gamma_u &:=\\begin{pmatrix} \\gamma^1 u_1 , \\gamma^2 u_2, ..., \\gamma^N u_N \\end{pmatrix}^t,\\\\\n", "\t\\gamma^0_{\\phi_e} &: =\\begin{pmatrix} \\gamma^{01} \\phi_e, \\gamma^{02} \\phi_e, ..., \\gamma^{0N} \\phi_e \\end{pmatrix}^t,\n", "\\end{aligned}$$\n", "with superscript $t$ denoting the transposition." ] }, { "cell_type": "markdown", "id": "ef8eac79-cbd6-43c9-9e0d-a026a54eb299", "metadata": {}, "source": [ "This is the system that it is solved." ] }, { "cell_type": "markdown", "id": "2364c530-b9f5-46df-ae36-01af72789635", "metadata": {}, "source": [ "## Preliminaries of the discretization" ] }, { "cell_type": "markdown", "id": "64eb9a2a-6b7f-46ed-81f8-9fcea6ddc325", "metadata": {}, "source": [ "### Spherical coordinate system" ] }, { "cell_type": "markdown", "id": "7feae07c-0df9-445a-a5ef-d5fb745754e3", "metadata": {}, "source": [ "A vector is written as $\\mathbf{r}=\\left(r,\\varphi,\\theta\\right)^t$, with $r \\in [0,\\infty)$, $\\varphi \\in [0,2\\pi)$ and $\\theta \\in [0,\\pi]$, which in Cartesian coordinates is equivalent to $\\mathbf{r}=r\\left(\\sin \\theta \\cos \\varphi,\\sin \\theta \\sin \\varphi,\\cos \\theta\\right)^t$. The unitary vectors of the spherical coordinate system can be written in Cartesian coordinates as\n", "$$\\begin{aligned}\n", " &\\widehat{\\mathbf{e}}_r= (\\sin \\theta \\cos \\varphi , \\sin \\theta \\sin \\varphi , \\cos \\theta )^t, \\\\\n", " &\\widehat{\\mathbf{e}}_\\theta=(\\cos \\theta \\cos \\varphi , \\cos \\theta \\sin \\varphi , -\\sin \\theta )^t, \\\\\n", " &\\widehat{\\mathbf{e}}_{\\varphi}=(-\\sin \\varphi , \\cos \\varphi , 0 )^t.\n", "\\end{aligned}$$\n", "Also, the gradient operator in spherical coordinates:\n", "$$\\begin{aligned}\n", " \\nabla f&=\\frac{\\partial f}{\\partial r} \\widehat{\\mathbf{e}}_r+\\frac{1}{r} \\frac{\\partial f}{\\partial \\theta} \\widehat{\\mathbf{e}}_\\theta+\\frac{1}{r \\sin \\theta} \\frac{\\partial f}{\\partial \\varphi} \\widehat{\\mathbf{e}}_{\\varphi}\n", "\\end{aligned}$$" ] }, { "cell_type": "markdown", "id": "2d53964d-bed6-4ae3-b38f-45f1b1b759e0", "metadata": {}, "source": [ "### Associated Legendre functions" ] }, { "cell_type": "markdown", "id": "670073a7-0033-443b-a9f1-9311f5ba0a5d", "metadata": {}, "source": [ "$P_l^m$ are the associated Legendre functions of degree $l$ and order $m$ defined as:\n", "$$P_{l}^m\\left(x\\right) := (-1)^m \\left( 1- x^2\\right)^{\\frac{m}{2}} \\frac{d^m}{dx^m}P_l(x), \\quad \\text{with} \\quad P_{l}\\left(x\\right) := \\frac{1}{2^ll!}\\frac{d^l}{dx^l}(x^2-1)^l.$$\n", "\n", "Here, the term $(-1)^m$ is the Condon-Shortley phase factor." ] }, { "cell_type": "markdown", "id": "62167d1f-7acd-470a-a1fd-fa2353e8e2af", "metadata": {}, "source": [ "### Real spherical harmonics" ] }, { "cell_type": "markdown", "id": "93447be0-c4f4-49c5-8126-f71b6d8511ea", "metadata": {}, "source": [ "Real spherical harmonics of degree $l$ and order $m$ are defined using spherical coordinates:\n", "$$\\begin{aligned}\n", "\t\t Y_{l,m}\\left(\\theta,\\varphi\\right) &:= \\sqrt{ (2-\\delta_{m,0}) \\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\theta\\right) \\cos m \\varphi , \\text{ and}\\\\\n", "\t\tY_{l,-m}\\left(\\theta,\\varphi\\right) &:= \\sqrt{ (2-\\delta_{m,0})\\frac{\\left(2l+1\\right)\\left(l-m\\right)!}{4 \\pi \\left(l+m\\right)!}} P_l^{m} \\left(\\cos\\theta\\right) \\sin m \\varphi ,\n", "\\end{aligned}$$\n", "with $l\\in \\mathbb{N}_0$, $m\\in \\mathbb{Z}$ such that $0\\leq m\\leq l$. If $m=0$, then $\\delta_{m,0}=1$, and it is zero otherwise." ] }, { "cell_type": "markdown", "id": "eb7f0453-4b70-4a32-980c-2979712657f8", "metadata": {}, "source": [ "### Orthonormality of spherical harmonics" ] }, { "cell_type": "markdown", "id": "49cf56dc-b8ea-438c-a499-a49d36bc6f47", "metadata": {}, "source": [ "Spherical harmonics are dense in $C(\\mathbb{S}^2)$, with $\\mathbb{S}^2$ the surface of the unit sphere, and form a complete orthonormal system in $L^2(\\mathbb{S}^2)$ with respect to the internal product defined by:\n", "$$\\left( \\psi , \\xi \\right)_{L^2(\\mathbb{S}^2)} = \\int_{0}^{2\\pi}\\int_{0}^{\\pi} \\psi\\left(\\theta,\\varphi\\right) \\xi\\left(\\theta,\\varphi\\right) \\sin\\left(\\theta\\right) d\\theta d\\varphi.$$\n", "\n", "They also are orthogonal in $H^1(\\mathbb{S}^2)$." ] }, { "cell_type": "markdown", "id": "02a1d5e7-0706-4562-b250-26d005c169ae", "metadata": {}, "source": [ "## Discretization" ] }, { "cell_type": "markdown", "id": "5c2a72a0-f8f9-45c9-b12a-bb217c7cdda6", "metadata": {}, "source": [ "Let be $j\\in \\{1,...,N\\}$. We define the reference system $j$ as the one centered at $\\mathbf{p_j}$ with the same orientation that the reference system centered in the origin. Furthermore, we denote by $Y_{l,m,j}$ the spherical harmonic $Y_{l,m}$ centered in the origin of the reference system $j$. Thus, if $\\left( r_j, \\varphi_j, \\theta_j \\right)$ are the vector spherical coordinates of $\\mathbf{r_j}$ in the reference system $j$, we have that $Y_{l,m,j}\\left(\\mathbf{r}_j\\right)=Y_{l,m}\\left(\\theta_j, \\varphi_j\\right)$." ] }, { "cell_type": "markdown", "id": "18770c93-5966-488f-aacf-25ac55f0e3bc", "metadata": {}, "source": [ "For $L \\in \\mathbb{N}_0$ and $j\\in \\{1,...,N\\}$, we define subspaces \n", "$$\\mathcal{Y}_L\\left(\\Gamma_j \\right):= \\text{span}\\left\\lbrace Y_{l,m,j}: l \\in \\mathbb{N}_0, m \\in \\mathbb{Z}, l \\leq L, |m|\\leq l \\right\\rbrace,$$\n", "equipped with the $L^2(\\Gamma_j)$-norm. Notice that the dimension of each subspace is $(L+1)^2$, and that the sequence of subspaces $\\lbrace \\mathcal{Y}_L \\left(\\Gamma_j \\right) \\rbrace_{L \\in \\mathbb{N}_0}$ is dense in $H^{\\frac{1}{2}}(\\Gamma_j)$ and in $H^{-\\frac{1}{2}}(\\Gamma_j)$. This result justifies the discretization of all boundary Dirichlet and Neumann unknowns with spherical harmonics." ] }, { "cell_type": "markdown", "id": "a677a41b-a5e1-4c6a-b673-9d4cc2c0d28c", "metadata": {}, "source": [ "For $j \\in \\lbrace 1, ..., N \\rbrace$, we write $u^L_{d,0j}$, $u^L_{n,0j}$, $u^L_{d,j}$ and $u^L_{n,j}$ in $\\mathcal{Y}_L(\\Gamma_j)$ for the approximations of $\\gamma_d^{0j} u_0$, $\\gamma_n^{0j} u_0$, $\\gamma_d^{j} u_j$ and $\\gamma_n^{j} u_j$, respectively. They can be written as the following series expansions:\n", "$$\\begin{aligned}\n", " u^L_{d,0j}&=\\sum_{l=0}^{L} \\sum_{m=-l}^l u^{l,m}_{d,0j} Y_{l,m,j}, & u^L_{n,0j} &=\\sum_{l=0}^{L} \\sum_{m=-l}^l u^{l,m}_{n,0j} Y_{l,m,j},\\\\\n", " u^L_{d,j}&=\\sum_{l=0}^{L} \\sum_{m=-l}^l u^{l,m}_{d,j} Y_{l,m,j},& u^L_{d,j} &=\\sum_{l=0}^{L} \\sum_{m=-l}^l u^{l,m}_{n,j} Y_{l,m,j},\n", "\\end{aligned}$$\n", "with $u^{l,m}_{d,0j}$, $u^{l,m}_{n,0j}$, $u^{l,m}_{d,j}$, and $u^{l,m}_{n,j}$ being constants." ] }, { "cell_type": "markdown", "id": "6bf46bed-ed01-4776-b466-fdbd9377d720", "metadata": {}, "source": [ "## Solving" ] }, { "cell_type": "markdown", "id": "bd6b3242-bc1b-4c6c-99f1-f5a3a9ac44f5", "metadata": {}, "source": [ "In the module `biosspheres.formulations.mtf.solvertemplates` there are two python functions to solve the presented problem. One uses a direct method to solve, and the other one an indirect one." ] }, { "cell_type": "markdown", "id": "84d48646-637c-4066-a059-56c5ded35ebd", "metadata": {}, "source": [ "### Import of the needed libraries" ] }, { "cell_type": "code", "execution_count": 33, "id": "6ad1c2e8-c0ba-413a-bbfb-ab1acc4c19af", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm, colors\n", "import biosspheres.formulations.mtf.solvertemplates as solver\n", "import biosspheres.quadratures.sphere as quadratures\n", "import biosspheres.miscella.spherearrangements as pos\n", "import biosspheres.laplace.drawing as draw" ] }, { "cell_type": "markdown", "id": "64f6b718-635e-48b4-b9fd-7d9800691d5e", "metadata": {}, "source": [ "### Definition of needed variables" ] }, { "cell_type": "markdown", "id": "d3d46e69-0d9a-409b-885f-00556574076e", "metadata": {}, "source": [ "We will need:\n", "- The number of spheres,\n", "- The maximum degree of spherical harmonics used to discretize each trace.\n", "- The degree parameter for the numerical quadrature.\n", "- An array with the radii of the spheres.\n", "- A list with the positions of the spheres.\n", "- An array with the values of $\\sigma_j$.\n", "- The vector $\\mathbf{p}$ of $\\phi_e$." ] }, { "cell_type": "markdown", "id": "35596c72-d599-43e4-aae4-9269ef7f3f2d", "metadata": {}, "source": [ "Definition of the number of spheres, it must be an **integer**:" ] }, { "cell_type": "code", "execution_count": 34, "id": "c00b6b07-0a9f-4a4d-b453-7fc66a920515", "metadata": {}, "outputs": [], "source": [ "n = 8" ] }, { "cell_type": "markdown", "id": "68f4557e-9c41-4fe8-a8d3-984ba87b9b2f", "metadata": {}, "source": [ "Definition of the maximum degree of spherical harmonics to be used, it must be an **integer**:" ] }, { "cell_type": "code", "execution_count": 35, "id": "92d8c3e2-e17f-4aa6-bf13-db794fe5b612", "metadata": {}, "outputs": [], "source": [ "big_l = 15" ] }, { "cell_type": "markdown", "id": "e261abef-042c-4105-b444-d4c8e1a7719a", "metadata": {}, "source": [ "Definition of the degree parameter for the numerical quadrature, it must be an **integer**:" ] }, { "cell_type": "code", "execution_count": 36, "id": "8335c394-c361-4d2e-bb09-cc5e798b01bf", "metadata": {}, "outputs": [], "source": [ "big_l_c = 55" ] }, { "cell_type": "markdown", "id": "d3d10afa-c308-4db6-83eb-0869759e4db3", "metadata": {}, "source": [ "Definition of the array with the radii of the spheres, it must be a **numpy array** of one dimension. In this case we are going to define all radius equal to a parameter named `r`." ] }, { "cell_type": "code", "execution_count": 37, "id": "e7fd1151-76df-430e-ae7f-e09e237c9fd5", "metadata": {}, "outputs": [], "source": [ "r = 0.875\n", "radii = np.ones(n) * r" ] }, { "cell_type": "markdown", "id": "5b6e2cff-bfbf-4f58-9c30-18888a9831c0", "metadata": {}, "source": [ "Definition of the list with the positions of the spheres, for this we use a existing routine:" ] }, { "cell_type": "code", "execution_count": 38, "id": "717faf59-6a6f-49bd-a815-21cb01901f4b", "metadata": {}, "outputs": [], "source": [ "d = 1.15\n", "center_positions = pos.cube_vertex_positions(int(n**(1/3)), r, d)" ] }, { "cell_type": "markdown", "id": "c15a309e-9289-4b07-afca-d8b3ad3cb2ff", "metadata": {}, "source": [ "We will plot the spheres to help visualizing them" ] }, { "cell_type": "code", "execution_count": 39, "id": "4fe59d68-e642-4277-985d-dbbd7fba3cde", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "quantity_theta_points, quantity_phi_points, weights, pre_vector = quadratures.gauss_legendre_trapezoidal_2d(50)\n", "vector = pre_vector * r\n", "fig = plt.figure()\n", "ax_1 = fig.add_subplot(111, projection='3d')\n", "for s in np.arange(0,n):\n", " ax_1.plot_surface(\n", " vector[0, :, :]+center_positions[s][0],\n", " vector[1, :, :]+center_positions[s][1],\n", " vector[2, :, :]+center_positions[s][2],\n", " rstride=1, cstride=1)\n", "ax_1.set_xlabel('$x$')\n", "ax_1.set_ylabel('$y$')\n", "ax_1.set_zlabel('$z$')\n", "ax_1.set_aspect('equal')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "de15653b-9e0d-4640-83ef-6de8f116c943", "metadata": {}, "source": [ "Definition of the numpy array containing $\\sigma_j$. In this example, we will make only $\\sigma_0$ different:" ] }, { "cell_type": "code", "execution_count": 40, "id": "adeda9c7-4e4b-49cd-ac77-5f6a79484294", "metadata": {}, "outputs": [], "source": [ "sigma_e = 1.75\n", "sigma_i = 0.75\n", "sigmas = np.ones(n+1) * sigma_i\n", "sigmas[0] = sigma_e" ] }, { "cell_type": "markdown", "id": "7254287e-a58b-498b-bc09-ec93472f82d8", "metadata": {}, "source": [ "Finally, the definition of the point source vector:" ] }, { "cell_type": "code", "execution_count": 41, "id": "69d3c35e-30f6-46a0-a926-263586c28a27", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-5., -5., -5.])" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p0 = np.ones(3)*-5.\n", "p0" ] }, { "cell_type": "markdown", "id": "379b6398-7729-4122-adaa-926e735422f0", "metadata": {}, "source": [ "### `mtf_laplace_n_spheres_point_source_direct_solver`" ] }, { "cell_type": "markdown", "id": "253a13ef-bad4-4eae-9d25-0e0a5ad4585e", "metadata": {}, "source": [ "Now, we solve using a direct solver:" ] }, { "cell_type": "code", "execution_count": 42, "id": "329f4ee9-4360-4b0f-afae-f43f9d637597", "metadata": {}, "outputs": [], "source": [ "traces = solver.mtf_laplace_n_spheres_point_source_direct_solver(n, big_l, big_l_c, radii, center_positions, sigmas, p0)" ] }, { "cell_type": "markdown", "id": "bac72951-a5bd-427d-8e0d-d8fe86c7d866", "metadata": {}, "source": [ "The solver used is `numpy.linalg.solve` from the `numpy` library." ] }, { "cell_type": "markdown", "id": "561ffb72-b8ef-457c-8e24-826f2712e781", "metadata": {}, "source": [ "The following is a plot of the exterior dirichlet traces:" ] }, { "cell_type": "code", "execution_count": 43, "id": "24510e71-799a-43f3-afc4-81ed28a65c23", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "quantity_theta_points, quantity_phi_points, \\\n", " weights, pre_vector, spherical_harmonics = \\\n", " quadratures.gauss_legendre_trapezoidal_real_sh_mapping_2d(\n", " big_l, big_l_c)\n", "vector = pre_vector * r\n", "num = (big_l + 1)**2\n", "surface_d0 = np.zeros((n, quantity_theta_points, quantity_phi_points))\n", "for s in np.arange(0, n):\n", " surface_d0[s, :, :] = np.sum(\n", " traces[num*s:num*(s+1), np.newaxis, np.newaxis]\n", " * spherical_harmonics, axis=0)\n", "surface_d0_max = np.max(np.abs(surface_d0))\n", "surface_d0 = (surface_d0 + surface_d0_max) / (2. * surface_d0_max)\n", "\n", "fig = plt.figure()\n", "ax_1 = fig.add_subplot(111, projection='3d')\n", "for s in np.arange(0,n):\n", " ax_1.plot_surface(\n", " vector[0, :, :]+center_positions[s][0],\n", " vector[1, :, :]+center_positions[s][1],\n", " vector[2, :, :]+center_positions[s][2],\n", " rstride=1, cstride=1, \n", " facecolors=cm.coolwarm(surface_d0[s, :, :]))\n", "ax_1.set_xlabel('$x$')\n", "ax_1.set_ylabel('$y$')\n", "ax_1.set_zlabel('$z$')\n", "ax_1.set_aspect('equal')\n", "fig.colorbar(cm.ScalarMappable(\n", " norm=colors.CenteredNorm(halfrange=surface_d0_max), cmap=cm.coolwarm),\n", " ax=ax_1)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2d74ecee-02ed-496d-8b4a-f11c6a51b159", "metadata": {}, "source": [ "### `mtf_laplace_n_spheres_point_source_indirect_solver`" ] }, { "cell_type": "markdown", "id": "c7d99913-892e-4e06-9eb8-00e0e88f2f6a", "metadata": {}, "source": [ "Now, we solve using the solver provided by `scipy.sparse.linalg.gmres`. This time, we have to specify a tolerance:" ] }, { "cell_type": "code", "execution_count": 44, "id": "c7886020-6a91-4cca-a9a8-56459234d3c9", "metadata": {}, "outputs": [], "source": [ "tolerance = 10**(-10)" ] }, { "cell_type": "code", "execution_count": 45, "id": "152f639a-fa0c-417d-9c45-37b3308f0e9d", "metadata": {}, "outputs": [], "source": [ "traces_2 = solver.mtf_laplace_n_spheres_point_source_indirect_solver(n, big_l, big_l_c, radii, center_positions, sigmas, p0, tolerance)" ] }, { "cell_type": "markdown", "id": "7560f4db-9f03-49d9-9971-4d0c16287d68", "metadata": {}, "source": [ "Let us see the difference between the solutions:" ] }, { "cell_type": "code", "execution_count": 46, "id": "86c2842d-1ffc-4f4e-81c0-93f1d1906f5b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.452772949383975e-13" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.norm(traces-traces_2)" ] }, { "cell_type": "markdown", "id": "0d2102ba-426d-4ddb-b5e0-e7a720bd42c9", "metadata": {}, "source": [ "In the notebook [mtf_times.ipynb](./mtf_times.ipynb) we measure the difference of time between routines (the iterative one for this example is faster)." ] }, { "cell_type": "markdown", "id": "86b217f5-e9bb-4cca-a381-ee9435b71fe6", "metadata": {}, "source": [ "### Plots using the representation formula" ] }, { "cell_type": "markdown", "id": "0ccede91-116b-4524-85d5-82566750c9d5", "metadata": {}, "source": [ "#### Cut in a plane" ] }, { "cell_type": "markdown", "id": "ead8afce-e2dd-45a8-960b-61cfc47a1c98", "metadata": {}, "source": [ "Center of the plot:" ] }, { "cell_type": "code", "execution_count": 47, "id": "72b1a95c-bee9-48fa-974f-763d61c025d3", "metadata": {}, "outputs": [], "source": [ "center = np.asarray([1., 1., 1.])*(r+d/2)" ] }, { "cell_type": "markdown", "id": "d7d2b4c9-5e8b-4e0b-9eaf-0bf9c9a3b202", "metadata": {}, "source": [ "Size of the window to be plotted:" ] }, { "cell_type": "code", "execution_count": 48, "id": "6a2df7fa-ee2f-443e-a77c-f223522e30b7", "metadata": {}, "outputs": [], "source": [ "horizontal = 10.\n", "vertical = 10." ] }, { "cell_type": "markdown", "id": "348c2ea5-7618-4261-bf22-e9dfdd272dcc", "metadata": {}, "source": [ "For the resolution of the image:" ] }, { "cell_type": "code", "execution_count": 49, "id": "c2a834e9-507d-407f-8ad6-437a59c6d733", "metadata": {}, "outputs": [], "source": [ "resolution = 50 # points per side\n", "inter_horizontal = resolution\n", "inter_vertical = resolution" ] }, { "cell_type": "markdown", "id": "e68e8cf4-8571-4bb8-b596-30061d25c280", "metadata": {}, "source": [ "If we do not want to plot the external function, we can use the following:" ] }, { "cell_type": "code", "execution_count": 50, "id": "476dc107-ecad-451c-a497-dec854d67ac9", "metadata": {}, "outputs": [], "source": [ "def zero(x: np.ndarray) -> float:\n", " return 0." ] }, { "cell_type": "code", "execution_count": 51, "id": "91e39095-7c29-404c-b81f-de9bee832aff", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cut = 1\n", "x1, y1, data = draw.draw_cut_representation_formula_n_sphere(cut, center,\n", " horizontal,\n", " vertical,\n", " inter_horizontal,\n", " inter_vertical,\n", " traces,\n", " radii,\n", " center_positions,\n", " big_l,\n", " zero)\n", "plt.figure()\n", "plt.imshow(data, origin='lower',\n", " extent=[-horizontal / 2 + center[1], horizontal / 2 + center[1],\n", " -vertical / 2 + center[2], vertical / 2 + center[2]],\n", " norm=colors.CenteredNorm()\n", " )\n", "plt.xlabel('$y$')\n", "plt.ylabel('$z$')\n", "plt.title('$x = $'+str(center[0]))\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": 52, "id": "f5767b42-e413-48b1-a915-bd91fda01919", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cut = 2\n", "x1, y1, data = draw.draw_cut_representation_formula_n_sphere(cut, center,\n", " horizontal,\n", " vertical,\n", " inter_horizontal,\n", " inter_vertical,\n", " traces,\n", " radii,\n", " center_positions,\n", " big_l,\n", " zero)\n", "plt.figure()\n", "plt.imshow(data, origin='lower',\n", " extent=[-horizontal / 2 + center[1], horizontal / 2 + center[1],\n", " -vertical / 2 + center[2], vertical / 2 + center[2]],\n", " norm=colors.CenteredNorm()\n", " )\n", "plt.xlabel('$x$')\n", "plt.ylabel('$z$')\n", "plt.title('$y = $'+str(center[1]))\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": 53, "id": "e7aaa882-be1a-4257-940c-c92945693c76", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cut = 3\n", "x1, y1, data = draw.draw_cut_representation_formula_n_sphere(cut, center,\n", " horizontal,\n", " vertical,\n", " inter_horizontal,\n", " inter_vertical,\n", " traces,\n", " radii,\n", " center_positions,\n", " big_l,\n", " zero)\n", "plt.figure()\n", "plt.imshow(data, origin='lower',\n", " extent=[-horizontal / 2 + center[1], horizontal / 2 + center[1],\n", " -vertical / 2 + center[2], vertical / 2 + center[2]],\n", " norm=colors.CenteredNorm()\n", " )\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.title('$z = $'+str(center[2]))\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": null, "id": "de7c3c35-1675-4c80-b28d-e71cdb8583ef", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "reqbiosspheresnotebooks", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.18" } }, "nbformat": 4, "nbformat_minor": 5 }